Completing Statements MCQs for Sub-Topics of Topic 4: Geometry

Question 1. A location with no dimension is called a:

(A) Line

(B) Plane

(C) Point

(D) Ray

Question 2. A geometric element that extends infinitely in both directions with no thickness is a:

(A) Line segment

(B) Line

(C) Ray

(D) Plane

Question 3. A flat surface that extends infinitely in all directions is a:

(A) Line

(B) Point

(C) Plane

(D) Space

Question 4. A part of a line with two distinct endpoints is called a:

(A) Ray

(B) Line

(C) Line segment

(D) Point

Question 5. A part of a line with one endpoint and extending infinitely in one direction is a:

(A) Line segment

(B) Ray

(C) Line

(D) Curve

Question 6. Two distinct lines in a plane that do not intersect are called:

(A) Intersecting lines

(B) Perpendicular lines

(C) Parallel lines

(D) Coincident lines

Question 7. Two lines in a plane that cross each other at exactly one point are called:

(A) Parallel lines

(B) Intersecting lines

(C) Skew lines

(D) Ray

Question 8. Three or more points that lie on the same line are called:

(A) Coplanar points

(B) Collinear points

(C) Vertex points

(D) Distinct points

Question 9. A simple closed curve made up entirely of line segments is a:

(A) Circle

(B) Polygon

(C) Ray

(D) Arc

Question 10. A set of points in space is represented by a:

(A) Line

(B) Plane

(C) Point

(D) Universe (or space itself)

Question 1. The measure of the distance between two points on a line segment is its:

(A) Width

(B) Length

(C) Area

(D) Perimeter

Question 2. The standard unit for measuring angles is the:

(A) Metre

(B) Kilogram

(C) Degree

(D) Second

Question 3. The common endpoint of the two rays forming an angle is its:

(A) Arm

(B) Vertex

(C) Side

(D) Interior

Question 4. The amount of rotation between the two arms of an angle is its:

(A) Size

(B) Measure

(C) Vertex

(D) Orientation

Question 5. The region between the two arms of an angle is called the:

(A) Exterior

(B) Vertex

(C) Interior

(D) Boundary

Question 6. A device used to measure angles is called a:

(A) Ruler

(B) Compass

(C) Protractor

(D) Scale

Question 7. To accurately measure a line segment using a ruler, one end should be placed at the:

(A) 1 cm mark

(B) Any mark

(C) Zero mark

(D) End of the ruler

Question 8. If two line segments have the same length, they are considered:

(A) Parallel

(B) Similar

(C) Congruent

(D) Perpendicular

Question 9. An angle of $180^\circ$ is called a:

(A) Right angle

(B) Obtuse angle

(C) Straight angle

(D) Reflex angle

Question 10. A complete angle measures:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 1. An angle measuring between $0^\circ$ and $90^\circ$ is classified as:

(A) Right

(B) Obtuse

(C) Acute

(D) Straight

Question 2. An angle that measures exactly $90^\circ$ is a:

(A) Acute angle

(B) Obtuse angle

(C) Right angle

(D) Straight angle

Question 3. An angle measuring between $90^\circ$ and $180^\circ$ is called a/an:

(A) Straight angle

(B) Right angle

(C) Acute angle

(D) Obtuse angle

Question 4. An angle measuring exactly $180^\circ$ is a:

(A) Reflex angle

(B) Complete angle

(C) Straight angle

(D) Zero angle

Question 5. An angle measuring more than $180^\circ$ but less than $360^\circ$ is a:

(A) Straight angle

(B) Reflex angle

(C) Obtuse angle

(D) Acute angle

Question 6. Lines that intersect at a right angle are called:

(A) Parallel lines

(B) Intersecting lines

(C) Perpendicular lines

(D) Skew lines

Question 7. A line perpendicular to a line segment at its midpoint is called a:

(A) Median

(B) Altitude

(C) Angle bisector

(D) Perpendicular bisector

Question 8. The symbol $\perp$ indicates:

(A) Parallelism

(B) Congruence

(C) Similarity

(D) Perpendicularity

Question 9. The corner of a square forms a:

(A) Acute angle

(B) Obtuse angle(C) Right angle

(D) Straight angle

Question 10. A zero angle measures:

(A) $90^\circ$

(B) $180^\circ$

(C) $0^\circ$

(D) $360^\circ$

Question 1. Two angles whose sum is $90^\circ$ are:

(A) Supplementary

(B) Adjacent

(C) Complementary

(D) Vertically opposite

Question 2. Two angles whose sum is $180^\circ$ are:

(A) Complementary

(B) Supplementary

(C) Adjacent

(D) Vertically opposite

Question 3. Adjacent angles whose non-common arms form a straight line constitute a:

(A) Complementary pair

(B) Supplementary pair

(C) Linear pair

(D) Vertically opposite pair

Question 4. Angles formed by two intersecting lines that are opposite to each other at the intersection are:

(A) Adjacent angles

(B) Corresponding angles

(C) Linear pair

(D) Vertically opposite angles

Question 5. Vertically opposite angles are always:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Adjacent

Question 6. If two adjacent angles are supplementary, they form a:

(A) Right angle

(B) Acute angle

(C) Linear pair

(D) Reflex angle

Question 7. If an angle measures $35^\circ$, its complement measures:

(A) $55^\circ$

(B) $145^\circ$

(C) $90^\circ$

(D) $180^\circ$

Question 8. If an angle measures $100^\circ$, its supplement measures:

(A) $80^\circ$

(B) $100^\circ$

(C) $260^\circ$

(D) $180^\circ$

Question 9. The sum of the angles in a linear pair is always:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 10. Two angles sharing a common vertex and a common arm, but no common interior points, are:

(A) Complementary angles

(B) Supplementary angles

(C) Adjacent angles

(D) Vertically opposite angles

Question 1. A line that intersects two or more lines at distinct points is a:

(A) Parallel line

(B) Perpendicular line

(C) Transversal

(D) Ray

Question 2. When a transversal intersects two lines, angles on opposite sides of the transversal and between the lines are called:

(A) Corresponding angles

(B) Alternate interior angles

(C) Consecutive interior angles

(D) Alternate exterior angles

Question 3. When a transversal intersects two lines, angles on the same side of the transversal and between the lines are called:

(A) Corresponding angles

(B) Alternate interior angles

(C) Consecutive interior angles

(D) Vertically opposite angles

Question 4. When a transversal intersects two lines, angles on the same side of the transversal, one interior and one exterior, are called:

(A) Alternate interior angles

(B) Consecutive exterior angles

(C) Corresponding angles

(D) Alternate exterior angles

Question 5. If a transversal intersects two parallel lines, then corresponding angles are:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Proportional

Question 6. If a transversal intersects two parallel lines, then alternate interior angles are:

(A) Supplementary

(B) Equal

(C) Complementary

(D) Consecutive

Question 7. If a transversal intersects two parallel lines, then consecutive interior angles are:

(A) Equal

(B) Complementary

(C) Supplementary

(D) Vertically opposite

Question 8. If a transversal intersects two lines such that corresponding angles are equal, then the lines are:

(A) Perpendicular

(B) Intersecting

(C) Parallel

(D) Skew

Question 9. If a transversal intersects two lines such that consecutive interior angles are supplementary, then the lines are:

(A) Intersecting

(B) Perpendicular

(C) Parallel

(D) Coincident

Question 10. If two lines are parallel, then alternate exterior angles formed by a transversal are:

(A) Supplementary

(B) Complementary

(C) Equal

(D) Adjacent

Question 1. Statements accepted as true without proof, used in a deductive system, are called:

(A) Theorems

(B) Definitions

(C) Axioms or Postulates

(D) Conjectures

Question 2. In Euclidean geometry, basic concepts like point, line, and plane are considered:

(A) Defined terms

(B) Theorems

(C) Undefined terms

(D) Axioms

Question 3. Statements assumed to be true that are specific to geometry are often called:

(A) Common notions

(B) Theorems

(C) Postulates

(D) Definitions

Question 4. Statements that are proven using definitions, axioms, and postulates are called:

(A) Axioms

(B) Postulates

(C) Theorems

(D) Conjectures

Question 5. Euclid's famous postulate regarding parallel lines is the:

(A) First Postulate

(B) Second Postulate

(C) Third Postulate

(D) Fifth Postulate

Question 6. The property that states "Things which are equal to the same thing are equal to one another" is an example of a/an:

(A) Definition

(B) Postulate

(C) Axiom

(D) Theorem

Question 7. Non-Euclidean geometries arise from modifying or replacing:

(A) Definitions

(B) Axioms

(C) Euclid's Fifth Postulate

(D) All postulates

Question 8. The process of logically deriving new true statements from existing ones is called:

(A) Definition

(B) Postulation

(C) Proof

(D) Conjecture

Question 9. According to Euclid's Postulate 1, a unique straight line can be drawn between:

(A) One point

(B) Two distinct points

(C) Three non-collinear points

(D) Any infinite number of points

Question 10. The sum of the angles in a Euclidean triangle is a consequence of:

(A) Definitions

(B) Axioms

(C) Postulates (including the Fifth)

(D) Undefined terms

Question 1. A simple closed curve made up only of line segments is defined as a:

(A) Circle

(B) Curve

(C) Polygon

(D) Ray

Question 2. The line segments that form the boundary of a polygon are called its:

(A) Diagonals

(B) Vertices

(C) Sides

(D) Angles

Question 3. The points where the sides of a polygon meet are its:

(A) Sides

(B) Diagonals

(C) Vertices

(D) Edges

Question 4. A line segment connecting two non-adjacent vertices of a polygon is a:

(A) Side

(B) Vertex

(C) Diagonal

(D) Edge

Question 5. A polygon with 4 sides is called a:

(A) Triangle

(B) Pentagon

(C) Hexagon

(D) Quadrilateral

Question 6. A polygon where all interior angles are less than $180^\circ$ is classified as:

(A) Concave polygon

(B) Regular polygon

(C) Convex polygon

(D) Irregular polygon

Question 7. A polygon with at least one interior angle greater than $180^\circ$ is a:

(A) Convex polygon

(B) Regular polygon

(C) Concave polygon

(D) Equilateral polygon

Question 8. A polygon that is both equilateral and equiangular is called a:

(A) Concave polygon

(B) Irregular polygon

(C) Regular polygon

(D) Simple polygon

Question 9. A triangle is a polygon with:

(A) 4 sides

(B) 3 sides

(C) 5 sides

(D) 2 sides

Question 10. The sum of the exterior angles of any convex polygon is always:

(A) $180^\circ$

(B) $360^\circ$

(C) $540^\circ$

(D) Depends on the number of sides

Question 1. A polygon with 3 sides is specifically called a:

(A) Quadrilateral

(B) Pentagon

(C) Triangle

(D) Hexagon

Question 2. The three line segments forming a triangle are known as its:

(A) Vertices

(B) Angles

(C) Sides

(D) Diagonals

Question 3. A triangle with all three sides of different lengths is a:

(A) Isosceles triangle

(B) Equilateral triangle

(C) Scalene triangle

(D) Right-angled triangle

Question 4. A triangle with exactly two sides of equal length is a:

(A) Scalene triangle

(B) Isosceles triangle

(C) Equilateral triangle

(D) Acute-angled triangle

Question 5. A triangle with all three sides of equal length is a:

(A) Isosceles triangle

(B) Scalene triangle

(C) Equilateral triangle

(D) Obtuse-angled triangle

Question 6. A triangle where all three angles are acute is called a/an:

(A) Right-angled triangle

(B) Obtuse-angled triangle

(C) Acute-angled triangle

(D) Equiangular triangle

Question 7. A triangle with one angle greater than $90^\circ$ is called a/an:

(A) Acute-angled triangle

(B) Right-angled triangle

(C) Obtuse-angled triangle

(D) Isosceles triangle

Question 8. A triangle with one angle exactly equal to $90^\circ$ is a/an:

(A) Acute-angled triangle

(B) Obtuse-angled triangle

(C) Right-angled triangle

(D) Equilateral triangle

Question 9. An equilateral triangle is also known as a/an:

(A) Scalene triangle

(B) Isosceles triangle

(C) Equiangular triangle

(D) Both B and C

Question 10. An isosceles right-angled triangle has angles measuring:

(A) $30^\circ, 60^\circ, 90^\circ$

(B) $45^\circ, 45^\circ, 90^\circ$

(C) $60^\circ, 60^\circ, 60^\circ$

(D) $90^\circ, 90^\circ, 0^\circ$

Question 1. The sum of the interior angles of any triangle is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 2. The measure of an exterior angle of a triangle is equal to the sum of the two:

(A) Adjacent interior angles

(B) Opposite interior angles

(C) All three interior angles

(D) Exterior angles

Question 3. In an isosceles triangle, the angles opposite the equal sides are:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Different

Question 4. The property that the sum of any two sides of a triangle is greater than the third side is known as the:

(A) Pythagorean Theorem

(B) Triangle Inequality Theorem

(C) Angle Sum Property

(D) Exterior Angle Property

Question 5. The side opposite the largest angle in a triangle is the:

(A) Smallest side

(B) Medium side

(C) Largest side

(D) Hypotenuse (only in right triangle)

Question 6. The angle opposite the shortest side in a triangle is the:

(A) Largest angle

(B) Smallest angle

(C) Medium angle

(D) A right angle (only in right triangle)

Question 7. In $\triangle$ABC, if $\angle A > \angle B$, then side BC is _____ side AC.

(A) Equal to

(B) Less than

(C) Greater than

(D) Parallel to

Question 8. If two angles of a triangle are equal, the sides opposite them are equal, which is the converse of the:

(A) Angle Sum Property

(B) Exterior Angle Property

(C) Triangle Inequality Theorem

(D) Isosceles Triangle Theorem

Question 9. The sum of an interior angle and its corresponding exterior angle at a vertex is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 10. If the angles of a triangle are in the ratio $1:2:3$, the angles are $30^\circ, 60^\circ,$ and:

(A) $90^\circ$

(B) $120^\circ$

(C) $45^\circ$

(D) $100^\circ$

Question 1. The Pythagorean theorem applies specifically to:

(A) Acute-angled triangles

(B) Obtuse-angled triangles

(C) Right-angled triangles

(D) All triangles

Question 2. In a right-angled triangle, the side opposite the right angle is the:

(A) Leg

(B) Altitude

(C) Hypotenuse

(D) Median

Question 3. According to the Pythagorean theorem, in a right triangle with legs a and b and hypotenuse c, the relationship is:

(A) $a + b = c$

(B) $a^2 + b^2 = c^2$

(C) $a^2 \times b^2 = c^2$

(D) $a^2 + c^2 = b^2$

Question 4. A set of three integers satisfying $a^2 + b^2 = c^2$ is called a:

(A) Geometric progression

(B) Arithmetic progression

(C) Pythagorean triplet

(D) Fibonacci sequence

Question 5. The converse of the Pythagorean theorem is used to determine if a triangle is:

(A) Isosceles

(B) Equilateral

(C) Right-angled

(D) Scalene

Question 6. If the sides of a triangle are $a, b, c$ and $a^2 + b^2 > c^2$, the angle opposite side c is:

(A) Obtuse

(B) Right

(C) Acute

(D) Straight

Question 7. If the sides of a triangle are $a, b, c$ and $a^2 + b^2 < c^2$, the angle opposite side c is:

(A) Acute

(B) Right

(C) Obtuse

(D) Reflex

Question 8. Finding the diagonal length of a rectangle is an application of the:

(A) Triangle Inequality

(B) Area Formula

(C) Pythagorean Theorem

(D) Perimeter Formula

Question 9. In a right triangle with legs 5 and 12, the hypotenuse is:

(A) $\sqrt{17}$

(B) 13

(C) 17

(D) $\sqrt{119}$

Question 10. In a right triangle with hypotenuse 13 and one leg 5, the other leg is:

(A) 8

(B) 12

(C) $\sqrt{194}$

(D) 18

Question 1. Two geometric figures having the same shape and the same size are:

(A) Similar

(B) Congruent

(C) Proportional

(D) Equivalent

Question 2. Two line segments are congruent if they have the same:

(A) Direction

(B) Position

(C) Length

(D) Endpoints

Question 3. Two angles are congruent if they have the same:

(A) Vertex

(B) Arms

(C) Measure

(D) Orientation

Question 4. The SSS criterion for triangle congruence states that if the three sides of one triangle are equal to the three corresponding sides of another, the triangles are:

(A) Similar

(B) Congruent

(C) Proportional

(D) Equilateral

Question 5. The SAS criterion requires two sides and the _____ angle to be equal for triangle congruence.

(A) Opposite

(B) Adjacent

(C) Included

(D) Any

Question 6. The ASA criterion requires two angles and the _____ side to be equal for triangle congruence.

(A) Opposite

(B) Adjacent

(C) Included

(D) Non-included

Question 7. The AAS criterion requires two angles and a _____ side to be equal for triangle congruence.

(A) Included

(B) Opposite

(C) Adjacent

(D) Non-included

Question 8. The RHS criterion is used specifically for _____ triangles.

(A) Acute-angled

(B) Obtuse-angled

(C) Right-angled

(D) Isosceles

Question 9. CPCTC is an acronym meaning Corresponding Parts of Congruent Triangles are:

(A) Calculated

(B) Congruent

(C) Complementary

(D) Corresponding

Question 10. If $\triangle \text{ABC} \cong \triangle \text{XYZ}$, then $\angle A$ is equal to:

(A) $\angle B$

(B) $\angle C$

(C) $\angle X$

(D) $\angle Y$

Question 1. Two geometric figures having the same shape but not necessarily the same size are:

(A) Congruent

(B) Proportional

(C) Similar

(D) Equal in area

Question 2. For two triangles to be similar, their corresponding angles must be:

(A) Proportional

(B) Complementary

(C) Supplementary

(D) Equal

Question 3. For two triangles to be similar, their corresponding sides must be:

(A) Equal

(B) Parallel

(C) Proportional

(D) Perpendicular

Question 4. The AA similarity criterion states that if two angles of one triangle are equal to two angles of another, the triangles are:

(A) Congruent

(B) Right-angled

(C) Similar

(D) Equilateral

Question 5. The SSS similarity criterion states that if the corresponding sides of two triangles are proportional, the triangles are:

(A) Congruent

(B) Similar

(C) Isosceles

(D) Scalene

Question 6. The SAS similarity criterion involves one equal angle and the sides _____ that angle being proportional.

(A) Opposite

(B) Adjacent to

(C) Not including

(D) Bisecting

Question 7. The Basic Proportionality Theorem (BPT) states that a line parallel to one side of a triangle divides the other two sides:

(A) Equally

(B) Proportionally

(C) Perpendicularly

(D) Congruently

Question 8. The converse of the BPT is used to prove that a line segment is _____ to a side of a triangle.

(A) Perpendicular

(B) Congruent

(C) Parallel

(D) Bisecting

Question 9. All equilateral triangles are always:

(A) Congruent

(B) Similar

(C) Isosceles but not similar

(D) Neither congruent nor similar

Question 10. Congruent triangles are always:

(A) Similar

(B) Only if they are equilateral

(C) Never similar

(D) Only if they are right-angled

Question 1. If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding:

(A) Angles

(B) Perimeters

(C) Sides

(D) Areas

Question 2. If the ratio of corresponding sides of two similar triangles is $m:n$, the ratio of their areas is:

(A) $m:n$

(B) $n:m$

(C) $m^2:n^2$

(D) $\sqrt{m}:\sqrt{n}$

Question 3. If the areas of two similar triangles are $a:b$, the ratio of their corresponding altitudes is:

(A) $a:b$

(B) $\sqrt{a}:\sqrt{b}$

(C) $a^2:b^2$

(D) $b:a$

Question 4. In a right-angled triangle, the altitude to the hypotenuse divides the triangle into smaller triangles that are _____ to the original triangle and to each other.

(A) Congruent

(B) Similar

(C) Equal in area

(D) Proportional

Question 5. Calculating the height of a tall object using its shadow length is an application of:

(A) Congruence of triangles

(B) Pythagorean theorem

(C) Similarity of triangles

(D) Area calculation

Question 6. If the ratio of perimeters of two similar triangles is $p:q$, the ratio of their areas is:

(A) $p:q$

(B) $p^2:q^2$

(C) $\sqrt{p}:\sqrt{q}$

(D) $q:p$

Question 7. If the ratio of areas of two similar triangles is 1:1, the triangles are:

(A) Only similar

(B) Congruent

(C) Isosceles

(D) Equilateral

Question 8. In right triangle ABC, right-angled at B, BD is altitude to AC. $\triangle \text{ADB}$ and $\triangle \text{BDC}$ are similar. The ratio AD/BD = ...

(A) AB/BC

(B) BD/DC

(C) AB/AC

(D) BD/BC

Question 9. If $\triangle \text{XYZ} \sim \triangle \text{PQR}$ with side ratio 2:1 (XY/PQ = 2), and Area($\triangle \text{PQR}$) = $A$, then Area($\triangle \text{XYZ}$) =

(A) $A$

(B) $2A$

(C) $4A$

(D) $A/2$

Question 10. Similarity is used in scale models where the linear dimensions are scaled by a factor, and the area is scaled by the _____ of that factor.

(A) Square

(B) Square root

(C) Cube

(D) Inverse

Question 1. A polygon with 4 sides is called a:

(A) Triangle

(B) Pentagon

(C) Hexagon

(D) Quadrilateral

Question 2. The sum of the interior angles of any convex quadrilateral is:

(A) $180^\circ$

(B) $360^\circ$

(C) $540^\circ$

(D) $720^\circ$

Question 3. A quadrilateral with exactly one pair of parallel sides is a:

(A) Parallelogram

(B) Rhombus

(C) Trapezium

(D) Kite

Question 4. A quadrilateral where both pairs of opposite sides are parallel is a:

(A) Trapezium

(B) Kite

(C) Parallelogram

(D) Square

Question 5. In a parallelogram, opposite angles are _____ and adjacent angles are _____.

(A) Equal, equal

(B) Supplementary, supplementary

(C) Equal, supplementary

(D) Supplementary, equal

Question 6. A parallelogram with all angles equal to $90^\circ$ is a:

(A) Rhombus

(B) Square

(C) Rectangle

(D) Trapezium

Question 7. A parallelogram with all sides equal is a:

(A) Rectangle

(B) Square

(C) Rhombus

(D) Kite

Question 8. A quadrilateral that is both a rectangle and a rhombus is a:

(A) Parallelogram

(B) Square

(C) Trapezium

(D) Kite

Question 9. In a rhombus, the diagonals are _____ and bisect each other.

(A) Equal

(B) Parallel

(C) Perpendicular

(D) Consecutive

Question 10. In a rectangle, the diagonals are _____ and bisect each other.

(A) Perpendicular

(B) Parallel

(C) Equal

(D) Opposite

Question 1. The Mid-Point Theorem states that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is:

(A) Equal to the third side

(B) Half of the third side

(C) Twice the third side

(D) Perpendicular to the third side

Question 2. In $\triangle$ABC, if D and E are midpoints of AB and AC, then DE is parallel to:

(A) AB

(B) AC

(C) BC

(D) AE

Question 3. The converse of the Mid-Point Theorem states that a line drawn through the midpoint of one side of a triangle, parallel to another side, intersects the third side at its:

(A) Vertex

(B) Endpoint

(C) Midpoint

(D) Any point

Question 4. If the length of the segment joining the midpoints of two sides of a triangle is 5 cm, the length of the third side is:

(A) 5 cm

(B) 2.5 cm

(C) 10 cm

(D) 20 cm

Question 5. The figure formed by joining the midpoints of the sides of any quadrilateral is always a:

(A) Square

(B) Rectangle

(C) Rhombus

(D) Parallelogram

Question 6. In $\triangle$PQR, S is the midpoint of PQ. A line through S parallel to QR intersects PR at T. Then T is the midpoint of:

(A) PQ

(B) QR

(C) PR

(D) ST

Question 7. If the figure formed by joining the midpoints of a quadrilateral is a rhombus, the diagonals of the original quadrilateral are:

(A) Equal

(B) Perpendicular

(C) Parallel

(D) Bisected

Question 8. If the figure formed by joining the midpoints of a quadrilateral is a rectangle, the diagonals of the original quadrilateral are:

(A) Perpendicular

(B) Parallel

(C) Equal

(D) Bisected

Question 9. The perimeter of the triangle formed by joining the midpoints of the sides of a triangle is _____ the perimeter of the original triangle.

(A) Equal to

(B) Half

(C) Twice

(D) One-fourth

Question 10. The area of the triangle formed by joining the midpoints of the sides of a triangle is _____ the area of the original triangle.

(A) Half

(B) One-third

(C) One-fourth

(D) Equal to

Question 1. The measure of the region enclosed by the boundary of a plane figure is called its:

(A) Perimeter

(B) Length

(C) Area

(D) Volume

Question 2. Two figures having the same area are said to be:

(A) Congruent

(B) Similar

(C) Equal in area

(D) Identical

Question 3. If two figures are congruent, then their areas are:

(A) Different

(B) Proportional

(C) Equal

(D) Zero

Question 4. Parallelograms on the same base and between the same parallels have:

(A) Different areas

(B) Equal areas

(C) Equal perimeters

(D) Equal diagonals

Question 5. Triangles on the same base and between the same parallels have:

(A) Different areas

(B) Equal areas

(C) Equal perimeters

(D) Equal sides

Question 6. If a triangle and a parallelogram are on the same base and between the same parallels, the area of the triangle is _____ the area of the parallelogram.

(A) Equal to

(B) Half

(C) Twice

(D) One-third

Question 7. If two triangles have the same area and the same base, they lie between the same:

(A) Lines

(B) Perpendiculars

(C) Parallels

(D) Vertices

Question 8. A diagonal of a parallelogram divides it into two triangles which are:

(A) Similar

(B) Equal in area

(C) Right-angled

(D) Obtuse-angled

Question 9. A median of a triangle divides it into two triangles which are:

(A) Congruent

(B) Similar

(C) Equal in area

(D) Equilateral

Question 10. If the area of a triangle is $A$, and a parallelogram is on the same base and between the same parallels, the area of the parallelogram is:

(A) $A/2$

(B) $A$

(C) $2A$

(D) $4A$

Question 1. The set of all points in a plane equidistant from a fixed point is a:

(A) Line

(B) Segment

(C) Circle

(D) Sphere

Question 2. The fixed point from which all points on a circle are equidistant is the:

(A) Radius

(B) Diameter

(C) Circumference

(D) Centre

Question 3. The fixed distance from the centre to any point on a circle is the:

(A) Diameter

(B) Chord

(C) Radius

(D) Arc

Question 4. A line segment joining any two points on the circle is a:

(A) Radius

(B) Diameter

(C) Chord

(D) Tangent

Question 5. A line segment passing through the centre of a circle with endpoints on the circle is a:

(A) Radius

(B) Chord

(C) Diameter

(D) Secant

Question 6. The longest chord of a circle is the:

(A) Radius

(B) Diameter

(C) Secant

(D) Tangent

Question 7. The distance around a circle is called its:

(A) Area

(B) Perimeter

(C) Circumference

(D) Both B and C

Question 8. A part of the circumference of a circle is called a/an:

(A) Chord

(B) Segment

(C) Sector

(D) Arc

Question 9. The region bounded by a chord and an arc is called a:

(A) Sector

(B) Segment

(C) Quadrant

(D) Semicircle

Question 10. The region bounded by two radii and an arc is called a:

(A) Segment

(B) Sector

(C) Chord

(D) Arc

Question 1. The angle subtended by a chord at the centre is _____ the angle subtended by the same chord at any point on the remaining part of the circle.

(A) Equal to

(B) Half

(C) Twice

(D) Thrice

Question 2. Equal chords of a circle subtend _____ angles at the centre.

(A) Complementary

(B) Supplementary

(C) Equal

(D) Proportional

Question 3. Chords equidistant from the centre of a circle are:

(A) Parallel

(B) Perpendicular

(C) Equal in length

(D) Unequal in length

Question 4. The perpendicular from the centre of a circle to a chord:

(A) Is parallel to the chord

(B) Bisects the chord

(C) Is equal to the radius

(D) Is longer than the chord

Question 5. The angle in a semicircle is always a:

(A) Acute angle

(B) Obtuse angle

(C) Right angle

(D) Straight angle

Question 6. Angles in the same segment of a circle are:

(A) Complementary

(B) Supplementary

(C) Equal

(D) Proportional

Question 7. If two chords subtend equal angles at the centre, then the chords are:

(A) Parallel

(B) Perpendicular

(C) Equal in length

(D) Different in length

Question 8. The line joining the centre of a circle to the midpoint of a chord is _____ to the chord.

(A) Parallel

(B) Perpendicular

(C) Equal in length

(D) Twice the length

Question 9. If the angle subtended by a chord at the circumference is $40^\circ$, the angle subtended at the centre is:

(A) $40^\circ$

(B) $80^\circ$

(C) $20^\circ$

(D) $100^\circ$

Question 10. The angle subtended by a diameter at any point on the circumference is:

(A) $0^\circ$

(B) $90^\circ$

(C) $180^\circ$

(D) $360^\circ$

Question 1. A quadrilateral whose all four vertices lie on a circle is called a:

(A) Parallelogram

(B) Rhombus

(C) Cyclic quadrilateral

(D) Trapezium

Question 2. In a cyclic quadrilateral, the sum of each pair of opposite angles is:

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 3. If the sum of any pair of opposite angles of a quadrilateral is $180^\circ$, then the quadrilateral is:

(A) A parallelogram

(B) A rhombus

(C) Cyclic

(D) A trapezium

Question 4. The exterior angle of a cyclic quadrilateral at a vertex is equal to the:

(A) Adjacent interior angle

(B) Opposite interior angle

(C) Sum of opposite interior angles

(D) Difference of opposite interior angles

Question 5. All rectangles are always:

(A) Similar

(B) Congruent

(C) Cyclic

(D) Rhombuses

Question 6. All squares are always:

(A) Rectangles

(B) Rhombuses

(C) Cyclic quadrilaterals

(D) All of the above

Question 7. If a parallelogram is cyclic, it must be a:

(A) Rhombus

(B) Square

(C) Rectangle

(D) Kite

Question 8. An isosceles trapezium can be a:

(A) Parallelogram

(B) Rhombus

(C) Cyclic quadrilateral

(D) Kite

Question 9. If ABCD is a cyclic quadrilateral, $\angle A + \angle C =$

(A) $90^\circ$

(B) $180^\circ$

(C) $270^\circ$

(D) $360^\circ$

Question 10. If the exterior angle at vertex A of cyclic quadrilateral ABCD is equal to the interior angle at vertex C, then the quadrilateral is:

(A) A parallelogram

(B) A cyclic quadrilateral

(C) A rectangle

(D) A rhombus

Question 1. A line that intersects a circle at exactly one point is a:

(A) Secant

(B) Chord

(C) Tangent

(D) Diameter

Question 2. A line that intersects a circle at two distinct points is a:

(A) Tangent

(B) Radius

(C) Secant

(D) Point of contact

Question 3. The point where a tangent touches a circle is called the:

(A) Vertex

(B) Centre

(C) Point of intersection

(D) Point of contact

Question 4. The radius drawn to the point of contact of a tangent is _____ to the tangent.

(A) Parallel

(B) Perpendicular

(C) Equal

(D) Double

Question 5. From a point outside a circle, _____ tangents can be drawn.

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 6. The lengths of the tangents drawn from an external point to a circle are:

(A) Unequal

(B) Complementary

(C) Supplementary

(D) Equal

Question 7. From a point inside a circle, _____ tangents can be drawn.

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 8. From a point on the circle, _____ tangent can be drawn.

(A) Zero

(B) One

(C) Two

(D) Infinite

Question 9. The line segment joining the points of contact of two parallel tangents is a:

(A) Radius

(B) Chord

(C) Diameter

(D) Secant

Question 10. The angle between a tangent and the radius through the point of contact is:

(A) $0^\circ$

(B) $45^\circ$

(C) $90^\circ$

(D) $180^\circ$

Question 1. A figure has line symmetry if it coincides with its original position after reflection across a:

(A) Point

(B) Line

(C) Plane

(D) Curve

Question 2. The line across which a figure is reflected to show line symmetry is called the:

(A) Centre of rotation

(B) Axis of symmetry

(C) Focal line

(D) Median

Question 3. Reflectional symmetry is also known as:

(A) Rotational symmetry

(B) Translational symmetry

(C) Line symmetry

(D) Point symmetry

Question 4. A square has _____ lines of symmetry.

(A) 1

(B) 2

(C) 3

(D) 4

Question 5. An equilateral triangle has _____ lines of symmetry.

(A) 1

(B) 2

(C) 3

(D) 4

Question 6. A circle has _____ lines of symmetry.

(A) 1

(B) A finite number

(C) Infinite

(D) 0

Question 7. A reflection is a type of rigid transformation because it preserves:

(A) Shape and size

(B) Orientation

(C) Colour

(D) Centre

Question 8. The reflection of a point $(x, y)$ across the $x$-axis is:

(A) $(-x, y)$

(B) $(x, -y)$

(C) $(-x, -y)$

(D) $(y, x)$

Question 9. The reflection of a point $(x, y)$ across the $y$-axis is:

(A) $(x, -y)$

(B) $(-x, y)$

(C) $(-x, -y)$

(D) $(y, x)$

Question 10. If a figure has line symmetry about a line, every point on the figure has its reflection also on the:

(A) Line of symmetry

(B) Exterior of the figure

(C) Figure itself

(D) Centre of the figure

Question 1. A figure has rotational symmetry if it coincides with its original position after a rotation less than $360^\circ$ about a fixed point called the:

(A) Axis of symmetry

(B) Point of reflection

(C) Centre of rotation

(D) Vertex

Question 2. The smallest angle of rotation (greater than $0^\circ$) that maps a figure onto itself is the:

(A) Order of rotation

(B) Angle of rotational symmetry

(C) Complete angle

(D) Straight angle

Question 3. The number of times a figure coincides with itself during a $360^\circ$ rotation is the:

(A) Angle of rotation

(B) Order of rotational symmetry

(C) Centre of rotation

(D) Magnitude of symmetry

Question 4. For a square, the order of rotational symmetry is:

(A) 1

(B) 2

(C) 3

(D) 4

Question 5. For a regular pentagon, the angle of rotational symmetry is:

(A) $60^\circ$

(B) $72^\circ$

(C) $90^\circ$

(D) $108^\circ$

Question 6. A figure with rotational symmetry of order 1 means it has no rotational symmetry other than the:

(A) $0^\circ$ rotation

(B) $90^\circ$ rotation

(C) $180^\circ$ rotation

(D) $360^\circ$ rotation

Question 7. If a figure has rotational symmetry of order $n$, the angle of rotational symmetry is:

(A) $n \times 360^\circ$

(B) $n / 360^\circ$

(C) $360^\circ / n$

(D) $360^\circ - n$

Question 8. A rectangle (not a square) has rotational symmetry of order:

(A) 1

(B) 2

(C) 3

(D) 4

Question 9. Which of the following shapes always has rotational symmetry (order > 1)?

(A) Scalene triangle

(B) Trapezium

(C) Parallelogram

(D) Kite

Question 10. The centre of rotation for a regular polygon is its:

(A) Vertex

(B) Midpoint of a side

(C) Geometric centre

(D) Any interior point

Question 1. 3-dimensional shapes have length, breadth, and:

(A) Area

(B) Perimeter

(C) Height (or Depth)

(D) Boundary

Question 2. The flat surfaces of a solid shape are called its:

(A) Edges

(B) Vertices

(C) Faces

(D) Sides

Question 3. The line segments where two faces of a solid shape meet are called its:

(A) Vertices

(B) Edges

(C) Faces

(D) Corners

Question 4. The points where edges of a solid shape meet are called its:

(A) Faces

(B) Edges

(C) Vertices

(D) Angles

Question 5. A solid shape with six rectangular faces is a:

(A) Cube

(B) Cylinder

(C) Cuboid

(D) Sphere

Question 6. A solid shape with six square faces is a:

(A) Cuboid

(B) Prism

(C) Cube

(D) Pyramid

Question 7. A solid shape with a circular base and a curved surface tapering to an apex is a:

(A) Cylinder

(B) Sphere

(C) Cone

(D) Pyramid

Question 8. A solid shape with two circular bases and a curved surface joining them is a:

(A) Cone

(B) Sphere

(C) Cylinder

(D) Prism

Question 9. A perfectly round solid shape where every point on the surface is equidistant from the centre is a:

(A) Circle

(B) Hemisphere

(C) Sphere

(D) Disc

Question 10. A pyramid has a polygonal base and triangular faces meeting at a common vertex called the:

(A) Base vertex

(B) Slant height

(C) Apex

(D) Edge

Question 1. Drawing a 3D solid on a flat surface is called:

(A) Plane geometry

(B) Solid geometry

(C) Visualising solid shapes

(D) Calculating volume

Question 2. A sketch where parallel lines remain parallel but angles are not preserved is a/an:

(A) Isometric sketch

(B) Orthographic projection

(C) Oblique sketch

(D) Perspective drawing

Question 3. A sketch representing a 3D solid by preserving true measurements along axes is a/an:

(A) Oblique sketch

(B) Orthographic projection

(C) Isometric sketch

(D) Cross-section

Question 4. Cutting a 3D solid with a plane gives a 2D shape called a:

(A) Net

(B) Surface

(C) Cross-section

(D) View

Question 5. If you slice a cube horizontally, the cross-section is a:

(A) Triangle

(B) Circle

(C) Square

(D) Hexagon

Question 6. If you slice a cylinder parallel to its base, the cross-section is a:

(A) Rectangle

(B) Circle

(C) Ellipse

(D) Triangle

Question 7. The Front View, Side View, and Top View of a 3D object are examples of:

(A) Oblique sketches

(B) Isometric sketches

(C) Orthographic projections

(D) Perspective drawings

Question 8. When drawing a Top View, you look at the object from:

(A) The front

(B) The side

(C) Above

(D) Below

Question 9. A 2D pattern that can be folded to form a 3D solid is called a:

(A) Cross-section

(B) View

(C) Net

(D) Surface

Question 10. Visualising different sections of a solid helps understand its:

(A) Surface area

(B) Volume

(C) Internal structure

(D) Perimeter

Question 1. A solid bounded by plane polygonal faces is called a:

(A) Sphere

(B) Cylinder

(C) Polyhedron

(D) Cone

Question 2. The faces of a polyhedron are:

(A) Curved surfaces

(B) Circles

(C) Polygons

(D) Ellipses

Question 3. A convex polyhedron is one where for every face, the polyhedron lies entirely on one side of the plane containing that:

(A) Edge

(B) Vertex

(C) Face

(D) Diagonal

Question 4. A polyhedron with faces made up of congruent regular polygons, where the same number of faces meet at each vertex, is a:

(A) Convex polyhedron

(B) Concave polyhedron

(C) Regular polyhedron (Platonic solid)

(D) Irregular polyhedron

Question 5. Euler's formula for convex polyhedra relates the number of vertices ($V$), edges ($E$), and faces ($F$) as:

(A) $V + E + F = 2$

(B) $V - E + F = 2$

(C) $E - V + F = 2$

(D) $V + E - F = 2$

Question 6. A cube is a convex polyhedron with $V=8$, $E=12$, $F=6$, satisfying:

(A) $V + E + F = 2$

(B) $V - E + F = 2$

(C) $E - V + F = 2$

(D) $V + E - F = 2$

Question 7. A triangular prism has 6 vertices and 9 edges. According to Euler's formula, it has _____ faces.

(A) 4

(B) 5

(C) 6

(D) 7

Question 8. If a convex polyhedron has 10 vertices and 15 edges, according to Euler's formula, it has _____ faces.

(A) 5

(B) 6

(C) 7

(D) 8

Question 9. Which of the following is NOT a polyhedron?

(A) Cube

(B) Cylinder

(C) Pyramid

(D) Prism

Question 10. How many Platonic solids are there in Euclidean geometry?

(A) 3

(B) 4

(C) 5

(D) 6