Assertion-Reason MCQs for Sub-Topics of Topic 5: Construction

Question 1. Assertion (A): To construct a circle with a diameter of $8 \text{ cm}$, you must set the compass opening to $4 \text{ cm}$.

Reason (R): The radius of a circle is always half of its diameter.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): A ruler marked in millimetres is the most suitable tool for constructing a line segment of exactly $5.7 \text{ cm}$ length.

Reason (R): A ruler allows for precise measurement and drawing of straight line segments.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): To copy a line segment PQ using a compass and ruler, you set the compass opening to the distance between P and Q.

Reason (R): A compass can maintain a fixed distance between its points, allowing for accurate transfer of lengths.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): A point is a basic geometric element that has definite length and width.

Reason (R): A point indicates only position in space.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): To construct a circle, you need to know its radius and circumference.

Reason (R): The radius and circumference are directly related properties of a circle.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): When constructing a line segment of a specific length using a ruler, it is best to start measuring from the very edge of the ruler.

Reason (R): The zero mark on most rulers is located at the extreme edge for convenience.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To construct a $60^\circ$ angle using a compass and ruler, you essentially construct an equilateral triangle.

Reason (R): All angles in an equilateral triangle measure $60^\circ$.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): Bisecting a $90^\circ$ angle gives two angles of $45^\circ$ each.

Reason (R): An angle bisector divides an angle into two equal parts.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): An angle of $40^\circ$ cannot be constructed using only compass and ruler by standard methods.

Reason (R): Only angles that are multiples of $15^\circ$ can be constructed with compass and ruler.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): To justify the angle bisector construction, we prove that any point on the constructed ray is equidistant from the vertex of the angle.

Reason (R): The property of an angle bisector is that any point on it is equidistant from the arms of the angle, not the vertex.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): An angle of $105^\circ$ can be constructed by combining constructions for $60^\circ$ and $45^\circ$ angles.

Reason (R): $60^\circ + 45^\circ = 105^\circ$, and both $60^\circ$ and $45^\circ$ are constructible angles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): The first step in bisecting any angle is to draw a ray from the vertex.

Reason (R): An angle bisector is a ray originating from the vertex that divides the angle.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To construct a perpendicular to a line at a point P on the line, you essentially construct a $90^\circ$ angle at P.

Reason (R): A perpendicular line makes a $90^\circ$ angle with the given line.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): The perpendicular bisector of a line segment passes through its midpoint.

Reason (R): The perpendicular bisector is defined as the line perpendicular to the segment that also passes through its midpoint.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): To construct the perpendicular bisector of segment AB, the radius of the arcs drawn from A and B must be greater than half the length of AB.

Reason (R): This ensures that the arcs intersect at two distinct points on either side of the segment.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): Any point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment.

Reason (R): This property is used in the justification of the perpendicular bisector construction, often proven using triangle congruence (e.g., SSS or SAS).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): There is only one line perpendicular to a given line that passes through a specific point not on the line.

Reason (R): The shortest distance from a point to a line is measured along the perpendicular segment.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): The construction of a perpendicular at a point on a line is equivalent to bisecting a straight angle.

Reason (R): A straight angle measures $180^\circ$, and its bisector forms two angles of $90^\circ$, which are perpendicular.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To construct a line parallel to a given line through a point not on it using corresponding angles, you must copy an angle.

Reason (R): If corresponding angles formed by a transversal are equal, then the lines are parallel.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): In the alternate interior angles method for constructing parallel lines, you draw a transversal and copy the alternate interior angle.

Reason (R): Alternate interior angles are formed on the same side of the transversal and between the two lines.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): According to the Parallel Postulate, through a point not on a given line, there is exactly one line parallel to the given line.

Reason (R): Geometric constructions are based on fundamental axioms and postulates.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): Copying an angle accurately is a necessary step in constructing parallel lines using angle properties.

Reason (R): The construction methods rely on creating a pair of equal corresponding or alternate interior angles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): Two lines in the same plane are parallel if they intersect at a $90^\circ$ angle.

Reason (R): Parallel lines never intersect.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): The converse of the Alternate Interior Angles Theorem is used to justify the parallel line construction method involving alternate interior angles.

Reason (R): The converse states that if alternate interior angles are equal, the lines are parallel.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To divide a line segment AB in the ratio $3:4$, you mark 7 equal points on a ray AC making an acute angle with AB.

Reason (R): The total number of equal parts on the auxiliary ray is the sum of the ratio terms ($m+n$).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): When dividing segment AB in ratio $m:n$ using ray AC, the parallel line is drawn through $A_m$ (the $m^{th}$ point on AC) parallel to $A_{m+n}B$.

Reason (R): This application of the Basic Proportionality Theorem ensures that AP:PB = $m:n$.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): The method of dividing a line segment in a given ratio relies on the properties of congruent triangles.

Reason (R): The justification for this construction primarily uses the Basic Proportionality Theorem, which involves similar triangles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): To divide a line segment into 5 equal parts, you can use the construction method for dividing a segment in the ratio $1:1:1:1:1$.

Reason (R): Dividing a segment into 'n' equal parts is a specific case of dividing it in the ratio $1:1:\dots:1$ (n times).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): When dividing a segment AB in ratio $m:n$ using ray AC, the angle formed by AC and AB must be acute.

Reason (R): Using an acute angle simplifies the visual clarity of the construction steps.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): A compass is used to mark equal distances on the auxiliary ray AC in the line segment division construction.

Reason (R): The compass ensures that the segments $AA_1, A_1A_2, \dots$ are all equal in length by maintaining a fixed radius.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): A triangle can be uniquely constructed if you are given the lengths of its three sides (SSS Criterion).

Reason (R): The SSS congruence criterion states that if three sides of one triangle are equal to the corresponding three sides of another triangle, then the triangles are congruent.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): To construct a triangle given two sides and the included angle (SAS Criterion), you must construct the angle first.

Reason (R): The included angle is located between the two given sides.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): You can always construct a triangle if you are given any three angle measures.

Reason (R): The sum of the angles in a triangle is always $180^\circ$.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): To construct a triangle with sides $3 \text{ cm}$, $4 \text{ cm}$, and $8 \text{ cm}$, you first draw the base of length $8 \text{ cm}$.

Reason (R): The sum of any two sides of a triangle must be greater than the third side (Triangle Inequality Theorem).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): To construct a triangle given two angles and a non-included side (AAS), you can first calculate the third angle using the angle sum property.

Reason (R): Knowing all three angles and one side reduces the AAS case to an ASA case, which is constructible.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): The minimum number of measurements required to uniquely construct any triangle is three.

Reason (R): SSS, SAS, ASA, and AAS criteria all require three measurements for unique determination (excluding specific cases like RHS or degenerate triangles).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): An equilateral triangle can be constructed by drawing a segment and then drawing arcs of the same length from both endpoints, intersecting above the segment.

Reason (R): This construction ensures that all three sides of the resulting triangle are equal to the length of the initial segment.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): To construct an isosceles triangle given the base and the equal sides, you use the SSS criterion.

Reason (R): The SSS criterion applies when the lengths of all three sides of the triangle are known.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): To construct a right-angled triangle when the hypotenuse and one leg are given, you can use the RHS congruence criterion.

Reason (R): The RHS criterion for constructing a right triangle requires the lengths of both legs to be known.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): An isosceles triangle with base angles of $60^\circ$ is always an equilateral triangle.

Reason (R): If two angles of a triangle are $60^\circ$, the third angle must also be $60^\circ$ by the angle sum property.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): To construct an isosceles triangle given the base and the vertex angle, you must first calculate the base angles.

Reason (R): In an isosceles triangle, the angles opposite the equal sides (base angles) are equal.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): A right-angled triangle can be constructed using the RHS criterion even if the given hypotenuse length is equal to the given leg length.

Reason (R): In any right-angled triangle, the hypotenuse is strictly longer than either leg.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To construct $\triangle ABC$ given BC, $\angle B$, and AB+AC, you draw BD = AB+AC on the ray forming $\angle B$ and construct the perpendicular bisector of CD.

Reason (R): Any point on the perpendicular bisector of CD is equidistant from C and D, which helps ensure AC = AD where A is the vertex on BD.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): To construct $\triangle ABC$ given BC, $\angle B$, and AB-AC (AB>AC), you draw BD = AB-AC on the ray forming $\angle B$ and construct the perpendicular bisector of CD.

Reason (R): This construction creates an isosceles triangle ADC where AC = AD, which helps satisfy the difference condition AB - AC = BD.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): To construct $\triangle ABC$ given $\angle B, \angle C$, and perimeter, you first draw a line segment equal to the perimeter and construct angles $\angle B$ and $\angle C$ at its ends.

Reason (R): The angles constructed at the ends of the perimeter segment should be half of $\angle B$ and $\angle C$ respectively to form isosceles triangles which relate the parts of the perimeter segment to the sides of the main triangle.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): Constructing a triangle given two sides and a median involves forming a parallelogram by extending the median.

Reason (R): Extending the median to twice its length and joining the endpoint to the vertices creates a parallelogram whose properties simplify the construction.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): To construct a triangle given two angles and an altitude, you first draw the altitude length and then construct the angles at the ends of the altitude.

Reason (R): The angles given are angles of the main triangle, not necessarily the angles formed by the altitude.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): In the perimeter construction (given $\angle B, \angle C$, Perimeter PQ), the point A is found by the intersection of angle arms, and then B and C are found using perpendicular bisectors of AP and AQ.

Reason (R): The perpendicular bisector property ensures that points B and C lie on the perimeter line PQ and satisfy BP = BA and CQ = CA respectively, thus summing to the correct perimeter and forming the triangle vertices.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To construct a triangle similar to $\triangle ABC$ with a scale factor $3/5$, you mark 5 equal parts on a ray from B and connect the $5^{th}$ point to C.

Reason (R): The denominator of the scale factor ($n$) determines the total number of equal parts to mark on the auxiliary ray when scaling down ($m < n$).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): If the scale factor for a similar triangle construction is $7/4$, the constructed triangle will be larger than the original triangle.

Reason (R): A scale factor greater than 1 results in an enlarged similar figure.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): The construction of similar triangles is justified by the Basic Proportionality Theorem (BPT).

Reason (R): BPT states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides the two sides proportionally, thus creating a similar triangle.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): When constructing a similar triangle with scale factor $m/n$, you always mark $m+n$ equal parts on the auxiliary ray.

Reason (R): The maximum number of equal parts needed on the auxiliary ray is $\text{max}(m, n)$ to connect to the endpoint of the original base and then draw a parallel line from the other index.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): After finding the point C' on BC (or extension), you draw a line through C' parallel to AC to find the vertex A'.

Reason (R): Drawing a parallel line ensures that the corresponding angles at A and A' (or C and C') are equal, maintaining similarity by AA criterion.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): If a similar triangle is constructed with a scale factor $k$, the ratio of the perimeters of the new triangle to the original triangle is $k^2$.

Reason (R): The ratio of the areas of two similar triangles is the square of the ratio of their corresponding sides (the scale factor).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): A general quadrilateral can be uniquely constructed if you are given the lengths of its four sides.

Reason (R): The shape of a quadrilateral with fixed side lengths can vary depending on the angles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): To uniquely construct a quadrilateral, you typically need 5 independent measurements.

Reason (R): A quadrilateral can be divided into two triangles by a diagonal, and a triangle requires 3 measurements for unique construction ($3+3=6$, but the diagonal is common, so $6-1=5$).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): A rectangle can be constructed if you are given its length and width.

Reason (R): A rectangle is a parallelogram with four right angles, and opposite sides are equal.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): To construct a rhombus given the lengths of its two diagonals, you draw the diagonals bisecting each other at right angles.

Reason (R): The diagonals of a rhombus bisect each other at right angles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): A square can be uniquely constructed if you are given the length of one side.

Reason (R): A square is a regular quadrilateral, meaning all sides are equal and all angles are equal (to $90^\circ$).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): To construct a parallelogram given two adjacent sides and the included angle, you can use the SAS criterion to construct one triangle.

Reason (R): A diagonal divides a parallelogram into two congruent triangles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): To construct a tangent to a circle at a point P on the circle, you draw a line perpendicular to the radius at P.

Reason (R): The radius through the point of contact is perpendicular to the tangent at that point.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): To construct tangents from an external point P to a circle with center O, you find the midpoint M of OP and draw a circle with radius OM.

Reason (R): This auxiliary circle intersects the original circle at the points of tangency because the angles subtended by the diameter OP at these points are $90^\circ$, making the radii perpendicular to the lines from P.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): The lengths of the two tangents drawn from an external point to a circle are always equal.

Reason (R): The line segment joining the center to the external point bisects the angle between the tangents and the chord joining the points of contact perpendicularly.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): From a point inside a circle, no tangents can be drawn.

Reason (R): A tangent intersects the circle at exactly one point, and any line through an interior point will intersect the circle at two points (a secant).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): To construct tangents from an external point P to a circle such that the angle between them is $60^\circ$, you must construct an angle of $120^\circ$ at the center.

Reason (R): The angle between the tangents from an external point and the angle between the radii to the points of contact are supplementary ($180^\circ$).

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): The justification for the tangent construction from an external point P involves showing that the angles formed at the points of intersection with the original circle are $90^\circ$.

Reason (R): A line segment from an external point to a point on the circle is a tangent if and only if it is perpendicular to the radius at that point.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 1. Assertion (A): Justification of a geometric construction is the process of explaining the steps taken to draw the figure.

Reason (R): Justification proves that the constructed figure possesses the required geometric properties based on axioms, postulates, and theorems.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 2. Assertion (A): Measurement with a ruler and protractor is a valid form of geometric justification.

Reason (R): Measurement provides numerical verification of the properties of a constructed figure.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 3. Assertion (A): The justification for constructing an angle bisector uses the property that any point on the bisector is equidistant from the arms of the angle.

Reason (R): This property is often proven using the SSS congruence criterion applied to triangles formed within the construction.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 4. Assertion (A): The justification for constructing parallel lines using alternate interior angles relies on the Basic Proportionality Theorem.

Reason (R): The Basic Proportionality Theorem relates to the proportionality of segments formed by a line parallel to one side of a triangle.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 5. Assertion (A): Congruence criteria (SSS, SAS, ASA, AAS, RHS) are essential tools for justifying many geometric constructions.

Reason (R): By proving the congruence of triangles formed during construction, we can establish that required properties (like side equality, angle equality, perpendicularity) are met.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 6. Assertion (A): An axiom is a statement that can be proven using theorems and postulates.

Reason (R): Axioms are fundamental truths accepted without proof, forming the basis of a geometric system.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) is false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.

Question 7. Assertion (A): The primary goal of geometric constructions is to develop precise drawing skills.

Reason (R): Geometric constructions help in understanding geometric concepts and developing logical reasoning skills by providing visual representations and requiring justification based on geometric principles.

(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

(B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

(C) Assertion (A) is true but Reason (R) is false.

(D) Assertion (A) false but Reason (R) is true.

(E) Both Assertion (A) and Reason (R) are false.