Matching Items MCQs for Sub-Topics of Topic 4: Geometry

(i) Point

(ii) Line

(iii) Plane

(iv) Line Segment

(v) Ray

(a) Part of a line with one endpoint and extends infinitely in one direction

(b) Extends infinitely in both directions with no breadth or thickness

(c) A location with no dimension

(d) A flat surface extending infinitely in all directions

(e) Part of a line with two definite endpoints

(i) Line AB

(ii) Ray AB (from A to B)

(iii) Line Segment AB

(iv) Point A

(v) Plane P

(a) P (Capital letter or script letter)

(b) $\overline{AB}$

(c) A single capital letter

(d) $\overrightarrow{AB}$

(e) $\overleftrightarrow{AB}$

(i) Point

(ii) Line

(iii) Plane

(iv) Space

(v) Line segment

(a) 3 dimensions

(b) 1 dimension

(c) 0 dimensions

(d) Depends on context (Line segment has length)

(e) 2 dimensions

(i) Parallel lines

(ii) Intersecting lines

(iii) Coincident lines

(iv) Skew lines

(v) Perpendicular lines

(a) Lines that lie in different planes and do not intersect

(b) Lines that meet at exactly one point, forming a $90^\circ$ angle

(c) Lines that lie in the same plane and never intersect

(d) Lines that are exactly the same line

(e) Lines that meet at exactly one point

(i) Open curve

(ii) Closed curve

(iii) Simple curve

(iv) Non-simple curve

(v) Polygon

(a) A simple closed curve made up of line segments

(b) A curve that starts and ends at the same point

(c) A curve that does not cross itself

(d) A curve that starts and ends at different points

(e) A curve that crosses itself

(i) Vertex

(ii) Arms (Sides)

(iii) Interior of an angle

(iv) Exterior of an angle

(v) Angle measure

(a) The amount of rotation between the two rays

(b) The common endpoint of the two rays forming the angle

(c) The two rays forming the angle

(d) The region outside the angle

(e) The region between the two rays, excluding the boundary

(i) Length of a line segment

(ii) Measure of an angle

(iii) Area of a plane figure

(iv) Volume of a solid

(v) Perimeter of a polygon

(a) Square metres ($\text{m}^2$)

(b) Metres (m)

(c) Degrees ($\circ$)

(d) Cubic metres ($\text{m}^3$)

(e) Units of length (e.g., cm)

(i) Measure length of a wall

(ii) Measure angle in a triangle

(iii) Draw a circle of a specific radius

(iv) Copy a line segment

(v) Check perpendicularity

(a) Set square

(b) Protractor

(c) Measuring tape

(d) Compass

(e) Ruler (and possibly compass/divider)

(i) Point B

(ii) Point on ray BA (not B)

(iii) Point between rays BA and BC

(iv) Point outside the angle region

(v) Point on ray BC (not B)

(a) In the exterior of the angle

(b) In the interior of the angle

(c) On the vertex of the angle

(d) On an arm of the angle

(e) On an arm of the angle

(i) $45^\circ$

(ii) $90^\circ$

(iii) $135^\circ$

(iv) $180^\circ$

(v) $270^\circ$

(a) Straight angle

(b) Acute angle

(c) Reflex angle

(d) Right angle

(e) Obtuse angle

(i) Acute angle

(ii) Right angle

(iii) Obtuse angle

(iv) Straight angle

(v) Reflex angle

(a) Exactly $180^\circ$

(b) $> 0^\circ$ and $< 90^\circ$

(c) $> 90^\circ$ and $< 180^\circ$

(d) $> 180^\circ$ and $< 360^\circ$

(e) Exactly $90^\circ$

(i) Perpendicular lines

(ii) Acute angle

(iii) Perpendicular bisector

(iv) Straight angle

(v) Obtuse angle

(a) An angle $> 90^\circ$ and $< 180^\circ$

(b) Lines intersecting at $90^\circ$

(c) An angle of $180^\circ$

(d) An angle $< 90^\circ$ (but $> 0^\circ$)

(e) A line perpendicular to a segment at its midpoint

(i) Right angle

(ii) Straight angle

(iii) Acute angle

(iv) Obtuse angle

(v) Complete angle

(a) The angle formed by a fully opened pair of scissors

(b) The angle at the corner of a book

(c) The angle formed by the minute hand of a clock in one full hour

(d) The angle formed by a slightly opened door

(e) The angle formed by the hands of a clock at 6:00 PM

(i) Right angle

(ii) Straight angle

(iii) Complete angle

(iv) Zero angle

(v) Reflex angle

(a) A full rotation

(b) An angle $> 180^\circ$

(c) No rotation

(d) Half a rotation

(e) Quarter of a rotation

(i) $\perp$

(ii) $\parallel$

(iii) $\cong$

(iv) $\sim$

(v) $\circ$

(a) Parallel

(b) Perpendicular

(c) Degrees (unit of angle measure)

(d) Similar

(e) Congruent

(i) Complementary angles

(ii) Supplementary angles

(iii) Angles in a linear pair

(iv) Angles around a point

(v) Vertically opposite angles

(a) Equal (not a fixed sum for all pairs)

(b) $90^\circ$

(c) $180^\circ$

(d) $360^\circ$

(e) $180^\circ$

(i) Adjacent angles

(ii) Linear pair

(iii) Vertically opposite angles

(iv) Complementary angles

(v) Supplementary angles

(a) Their sum is $180^\circ$

(b) Share a common vertex and a common arm

(c) Their sum is $90^\circ$

(d) Are always equal

(e) Adjacent angles whose non-common arms form a straight line

(i) $90^\circ$

(ii) $180^\circ$

(iii) $360^\circ$

(iv) Equal measures

(v) Measures greater than $90^\circ$

(a) Vertically opposite angles

(b) Complementary angles

(c) Supplementary angles (can be one obtuse, one acute)

(d) Angles around a point

(e) Linear pair

(i) Two adjacent angles whose sum is $90^\circ$

(ii) Two adjacent angles whose sum is $180^\circ$

(iii) Two non-adjacent angles formed by intersecting lines

(iv) Two angles whose measures add up to $90^\circ$

(v) Two angles whose measures add up to $180^\circ$

(a) Supplementary angles

(b) Complementary angles (adjacent or not)

(c) Vertically opposite angles

(d) Adjacent complementary angles

(e) A linear pair

(i) $30^\circ$

(ii) $45^\circ$

(iii) $60^\circ$

(iv) $80^\circ$

(v) $x^\circ$

(a) $90^\circ - x^\circ$

(b) $10^\circ$

(c) $30^\circ$

(d) $45^\circ$

(e) $60^\circ$

(i) Corresponding angles

(ii) Alternate interior angles

(iii) Consecutive interior angles

(iv) Alternate exterior angles

(v) Vertically opposite angles

(a) On opposite sides of the transversal, outside the lines

(b) On the same side of the transversal, between the lines

(c) Angles opposite each other at an intersection (not dependent on transversal)

(d) On opposite sides of the transversal, between the lines

(e) On the same side of the transversal, one interior and one exterior

(i) Corresponding angles are equal

(ii) Alternate interior angles are equal

(iii) Consecutive interior angles are supplementary

(iv) Lines are parallel

(v) Lines are not parallel

(a) Alternate exterior angles are unequal

(b) Alternate interior angles are equal

(c) The two lines are parallel

(d) The two lines are parallel

(e) The two lines are parallel

(i) Corresponding angles

(ii) Alternate interior angles

(iii) Consecutive interior angles

(iv) Alternate exterior angles

(v) Interior angles on the same side

(a) Are equal

(b) Are supplementary

(c) Are equal

(d) Are equal

(e) Are supplementary

(i) $\angle 1 = \angle 5$ (Corresponding angles)

(ii) $\angle 3 = \angle 6$ (Alternate interior angles)

(iii) $\angle 4 + \angle 6 = 180^\circ$ (Consecutive interior angles)

(iv) $\angle 2 = \angle 7$ (Alternate exterior angles)

(v) $\angle 1 + \angle 2 = 180^\circ$ (Linear pair)

(a) l || m

(b) l || m

(c) l and t intersect

(d) l || m

(e) l || m

(i) Transversal

(ii) Parallel lines

(iii) Intersecting lines

(iv) Corresponding angles test

(v) Interior angles on same side test

(a) Lines that never meet in a plane

(b) A line that crosses two or more other lines at distinct points

(c) If a pair sums to $180^\circ$, the lines are parallel

(d) Lines that meet at one point

(e) If a pair is equal, the lines are parallel

(i) Undefined Term

(ii) Definition

(iii) Axiom/Common Notion

(iv) Postulate

(v) Theorem

(a) A statement proven true using logical reasoning

(b) A statement assumed to be true, specific to geometry

(c) A basic concept accepted without definition (like Point, Line, Plane)

(d) Explains the meaning of a term

(e) A statement assumed to be true, generally applicable

(i) Postulate 1

(ii) Postulate 2

(iii) Postulate 3

(iv) Postulate 4

(v) Postulate 5

(a) A circle can be described with any centre and radius

(b) If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles

(c) All right angles are equal to one another

(d) To draw a straight line from any point to any point

(e) To produce a terminated line indefinitely in a straight line

(i) Things equal to the same thing are equal to one another

(ii) If equals be added to equals, the wholes are equal

(iii) If equals be subtracted from equals, the remainders are equal

(iv) Things which coincide with one another are equal to one another

(v) The whole is greater than the part

(a) If $a=b$ and $b=c$, then $a=c$

(b) If $a=b$, then $a+c = b+c$

(c) If $a=b$, then $a-c = b-c$

(d) Congruent figures have the same measure

(e) A subset is smaller than the set it belongs to

(i) Undefined term

(ii) Definition

(iii) Postulate

(iv) Axiom

(v) Theorem

(a) A straight line is one which lies evenly with the points on itself

(b) Through a point not on a given line, exactly one parallel line can be drawn (Playfair's Axiom, equivalent to Postulate 5)

(c) The sum of angles in a triangle is $180^\circ$

(d) Point

(e) Things equal to the same thing are equal to one another

(i) Two distinct points

(ii) Three non-collinear points

(iii) Euclid's Fifth Postulate

(iv) All right angles are equal

(v) Plane

(a) Defines a unique plane

(b) The foundation for parallel lines and related angle properties

(c) Can draw a unique straight line through them

(d) Ensures that all $90^\circ$ angles have the same measure

(e) A 2-dimensional surface

(i) Triangle

(ii) Quadrilateral

(iii) Pentagon

(iv) Hexagon

(v) Octagon

(a) 4 sides

(b) 6 sides

(c) 3 sides

(d) 8 sides

(e) 5 sides

(i) Side

(ii) Vertex

(iii) Diagonal

(iv) Interior angle

(v) Exterior angle

(a) The angle formed inside the polygon at a vertex

(b) A line segment connecting two adjacent vertices

(c) A point where two sides meet

(d) A line segment connecting two non-adjacent vertices

(e) The angle formed by one side and the extension of an adjacent side

(i) Convex polygon

(ii) Concave polygon

(iii) Regular polygon

(iv) Irregular polygon

(v) Equilateral polygon

(a) At least one interior angle $> 180^\circ$

(b) All interior angles $< 180^\circ$

(c) All sides are equal

(d) Both equilateral and equiangular

(e) Not a regular polygon

(i) Triangle

(ii) Square

(iii) Rectangle (not a square)

(iv) Rhombus (not a square)

(v) Pentagon

(a) A regular quadrilateral

(b) Has 5 sides

(c) A polygon with minimum number of sides

(d) A polygon that is equiangular but not equilateral

(e) A polygon that is equilateral but not equiangular

(i) Sum of interior angles

(ii) Sum of exterior angles (convex)

(iii) Number of diagonals

(iv) Measure of each interior angle (regular)

(v) Measure of each exterior angle (regular)

(a) $\frac{360^\circ}{n}$

(b) $360^\circ$

(c) $\frac{(n-2) \times 180^\circ}{n}$

(d) $(n-2) \times 180^\circ$

(e) $\frac{n(n-3)}{2}$

(i) Scalene triangle

(ii) Isosceles triangle

(iii) Equilateral triangle

(iv) Right-angled isosceles triangle

(v) Acute-angled triangle

(a) All three sides are equal

(b) All three angles are acute

(c) Exactly two sides are equal

(d) All three sides are of different lengths

(e) Has a right angle and two equal sides

(i) Acute-angled triangle

(ii) Obtuse-angled triangle

(iii) Right-angled triangle

(iv) Equiangular triangle

(v) Isosceles triangle

(a) One angle is exactly $90^\circ$

(b) All three angles are equal ($60^\circ$ each)

(c) One angle is greater than $90^\circ$

(d) At least two sides are equal

(e) All three angles are less than $90^\circ$

(i) Sides are 3 cm, 4 cm, 5 cm

(ii) Sides are 5 cm, 5 cm, 8 cm

(iii) Sides are 6 cm, 6 cm, 6 cm

(iv) Angles are $30^\circ, 60^\circ, 90^\circ$

(v) Angles are $20^\circ, 40^\circ, 120^\circ$

(a) Obtuse-angled triangle

(b) Equilateral triangle

(c) Right-angled triangle

(d) Isosceles triangle

(e) Scalene triangle

(i) All angles are equal

(ii) Angles opposite equal sides are equal

(iii) No two sides are equal

(iv) One angle is $90^\circ$

(v) Can have angles $45^\circ, 45^\circ, 90^\circ$

(a) Scalene

(b) Isosceles

(c) Right-angled isosceles

(d) Right-angled

(e) Equilateral

(i) Interior of the triangle

(ii) Exterior of the triangle

(iii) Boundary of the triangle

(iv) Vertex

(v) Side

(a) A line segment forming the triangle's edge

(b) The region outside the triangle

(c) The triangle itself (union of sides)

(d) A point where two sides meet

(e) The region inside the triangle

(i) Angle Sum Property

(ii) Exterior Angle Property

(iii) Isosceles Triangle Theorem

(iv) Converse of Isosceles Triangle Theorem

(v) Triangle Inequality Theorem

(a) The sum of two sides is greater than the third side

(b) Angles opposite equal sides are equal

(c) The sum of interior angles is $180^\circ$

(d) If two angles are equal, sides opposite them are equal

(e) Exterior angle equals sum of two opposite interior angles

(i) $50^\circ, 70^\circ$

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

(iii) $30^\circ, 110^\circ$

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

(v) $10^\circ, 20^\circ$

(a) $150^\circ$

(b) $40^\circ$

(c) $80^\circ$

(d) $45^\circ$

(e) $60^\circ$

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

(ii) $a^2 + b^2 > c^2$

(iii) $a^2 + b^2 < c^2$

(iv) $a+b > c$ (and satisfies i)

(v) $a+b > c$ (and satisfies ii)

(a) Obtuse angle

(b) Right angle

(c) Forms a triangle (not a specific angle type)

(d) Acute angle

(e) Cannot form a triangle (collinear points)

(i) Largest angle

(ii) Smallest angle

(iii) Equal angles

(iv) Angle is $90^\circ$

(v) Angles are $60^\circ$

(a) Opposite equal sides

(b) Opposite the hypotenuse

(c) Opposite the smallest side

(d) Opposite the largest side

(e) Opposite equal sides (in equilateral triangle)

(i) Checking if sides 3, 4, 8 can form a triangle

(ii) Finding the third angle of a triangle given two angles

(iii) Finding an unknown opposite interior angle given the exterior angle and one opposite interior angle

(iv) Determining if a triangle with equal base angles has equal sides

(v) Determining if a triangle with sides 6, 8, 10 is right-angled

(a) Converse of Isosceles Triangle Theorem

(b) Pythagorean Theorem (Converse)

(c) Triangle Inequality Theorem

(d) Angle Sum Property

(e) Exterior Angle Property

(i) Pythagorean Theorem

(ii) Converse of Pythagorean Theorem

(iii) Hypotenuse

(iv) Leg

(v) Pythagorean Triplet

(a) A set of three integers that satisfy $a^2 + b^2 = c^2$

(b) Applies only to right-angled triangles

(c) Used to prove if a triangle is right-angled

(d) One of the two sides forming the right angle

(e) The side opposite the right angle

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

(ii) $a^2 + b^2 > c^2$

(iii) $a^2 + b^2 < c^2$

(iv) $a+b > c$ (and satisfies i)

(v) $a+b > c$ (and satisfies ii)

(a) Obtuse-angled triangle

(b) Right-angled triangle

(c) Acute-angled triangle

(d) Right-angled triangle (also forms a triangle)

(e) Acute-angled triangle (also forms a triangle)

(i) Legs 3, 4; Hypotenuse = ?

(ii) Legs 5, 12; Hypotenuse = ?

(iii) Hypotenuse 13, Leg 5; Other leg = ?

(iv) Hypotenuse 10, Leg 6; Other leg = ?

(v) Equal legs 7, 7; Hypotenuse = ?

(a) $\sqrt{98}$ or $7\sqrt{2}$

(b) 13

(c) 5

(d) 12

(e) 8

(i) Finding the length of a ladder against a wall

(ii) Finding the shortest distance between two points in a grid

(iii) Finding the diagonal of a rectangular field

(iv) Calculating the slant height of a cone (given height and radius)

(v) Checking if a building corner is square ($90^\circ$)

(a) Applied to find the hypotenuse of a right triangle

(b) Applied to find one side of a right triangle

(c) Applied using the distance formula, derived from Pythagoras

(d) Applied using the converse of the theorem

(e) Applied to find the hypotenuse of a right triangle

(i) (3, 4, 5)

(ii) (5, 12, 13)

(iii) (8, 15, 17)

(iv) (7, 24, 25)

(v) (20, 21, 29)

(a) (14, 48, 50)

(b) (10, 24, 26)

(c) (16, 30, 34)

(d) (6, 8, 10)

(e) (40, 42, 58)

(i) Congruent figures

(ii) Congruent line segments

(iii) Congruent angles

(iv) Congruent triangles

(v) CPCTC

(a) Triangles whose corresponding sides and angles are equal

(b) Figures that have the same shape and size

(c) Line segments that have the same length

(d) Corresponding Parts of Congruent Triangles are Congruent

(e) Angles that have the same measure

(i) Side-Side-Side

(ii) Side-Angle-Side

(iii) Angle-Side-Angle

(iv) Angle-Angle-Side

(v) Right angle-Hypotenuse-Side

(a) AAS (Two angles and a non-included side)

(b) SSS (All three sides)

(c) SAS (Two sides and the included angle)

(d) RHS (Right angle, hypotenuse, and one side)

(e) ASA (Two angles and the included side)

(i) Two ₹ 5 coins from the same mint batch

(ii) A photograph and its enlarged copy

(iii) Two squares with sides 5 cm and 6 cm

(iv) Two equilateral triangles with side length 8 cm

(v) A triangle and its reflection

(a) Not congruent

(b) Congruent

(c) Not congruent

(d) Congruent

(e) Congruent

(i) Vertex A

(ii) Side BC

(iii) Angle B

(iv) Side AC

(v) Angle C

(a) $\angle Q$

(b) Side QR

(c) $\angle R$

(d) Vertex P

(e) Side PR

(i) AB=DE, BC=EF, CA=FD

(ii) AB=DE, $\angle B=\angle E$, BC=EF

(iii) $\angle B=\angle E$, BC=EF, $\angle C=\angle F$

(iv) $\angle A=\angle D$, $\angle B=\angle E$, BC=EF

(v) $\angle B=90^\circ$, $\angle E=90^\circ$, AC=DF, AB=DE

(a) ASA

(b) AAS

(c) SAS

(d) SSS

(e) RHS

(i) Similar figures

(ii) Similarity ratio

(iii) Corresponding angles (in similar triangles)

(iv) Corresponding sides (in similar triangles)

(v) Basic Proportionality Theorem

(a) Are proportional

(b) A line parallel to one side of a triangle divides the other two sides proportionally

(c) Figures that have the same shape but not necessarily the same size

(d) Are equal

(e) The ratio of the lengths of corresponding sides

(i) Angle-Angle

(ii) Side-Side-Side (Proportionality)

(iii) Side-Angle-Side (Proportionality)

(iv) Converse of BPT

(v) AA criterion consequence

(a) SSS ($\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$)

(b) If $\angle A = \angle D$ and $\angle B = \angle E$, then $\triangle \text{ABC} \sim \triangle \text{DEF}$

(c) AA (Two angles are equal)

(d) SAS ($\frac{AB}{DE} = \frac{AC}{DF}$ and $\angle A = \angle D$)

(e) If a line divides two sides proportionally, it is parallel to the third side

(i) Sides ratio 2:3

(ii) Sides ratio 1:2

(iii) Sides ratio m:n

(iv) Area ratio 9:16

(v) Perimeter ratio 4:5

(a) Area ratio $m^2:n^2$, Perimeter ratio $m:n$

(b) Sides ratio 3:4

(c) Area ratio 4:9, Perimeter ratio 2:3

(d) Area ratio 1:4, Perimeter ratio 1:2

(e) Area ratio 16:25, Perimeter ratio 4:5

(i) DE || BC

(ii) $\frac{AD}{DB} = \frac{AE}{EC}$

(iii) D and E are midpoints

(iv) $\angle ADE = \angle B$ and $\angle AED = \angle C$

(v) $\triangle \text{ADE} \sim \triangle \text{ABC}$

(a) DE || BC and DE = $\frac{1}{2}$ BC (Mid-Point Theorem)

(b) $\triangle \text{ADE} \sim \triangle \text{ABC}$ by AA similarity

(c) DE || BC (Converse of BPT)

(d) $\triangle \text{ADE} \sim \triangle \text{ABC}$

(e) $\frac{AD}{DB} = \frac{AE}{EC}$ (BPT)

(i) All equilateral triangles

(ii) Two right-angled triangles (if one acute angle of one equals one acute angle of the other)

(iii) A triangle and a smaller triangle formed by a line parallel to its base

(iv) Two triangles with proportional sides

(v) Two triangles with two pairs of equal angles

(a) Similar by SSS criterion

(b) Always similar

(c) Similar by AA criterion

(d) Are similar

(e) Similar by AA criterion (as they have a $90^\circ$ angle too)

(i) Ratio of areas

(ii) Ratio of perimeters

(iii) Ratio of altitudes

(iv) Ratio of medians

(v) Ratio of angle bisectors

(a) $k$

(b) $k^2$

(c) $k$

(d) $k$

(e) $k$

(i) Area ratio 25:81

(ii) Sides ratio 1:4

(iii) Perimeter ratio 3:7

(iv) Altitudes ratio 5:6

(v) Areas $36 \text{ cm}^2$ and $100 \text{ cm}^2$

(a) Area ratio 9:49

(b) Sides ratio 5:9

(c) Sides ratio 6:10 or 3:5

(d) Area ratio 25:36

(e) Area ratio 1:16

(i) Finding building height from shadow length

(ii) Calculating diagonal of a rectangle

(iii) Determining the actual area of a map region

(iv) Proving BD$^2$ = AD $\times$ DC in a right triangle altitude

(v) Making a scale model of a car

(a) Pythagorean Theorem

(b) Similarity of triangles (areas)

(c) Similarity in right triangles

(d) Similarity of triangles (sides and angles)

(e) Similarity of triangles (sides)

(i) Two similar triangles with side ratio 1:1

(ii) Altitude drawn to the hypotenuse of a right triangle

(iii) Area ratio of similar triangles is 1:1

(iv) Sides of two similar triangles are 6, 8, 10 and 3, 4, 5

(v) Two figures having the same shape

(a) The triangles are congruent

(b) The figures are similar

(c) The triangles are congruent

(d) The smaller triangles formed are similar to the original

(e) The similarity ratio is 2:1

(i) Median from A

(ii) Altitude from B

(iii) Angle bisector of C

(iv) Perimeter of $\triangle \text{ABC}$

(v) Area of $\triangle \text{ABC}$

(a) $k \times$ Altitude from Q

(b) $k^2 \times$ Area of $\triangle \text{PQR}$

(c) $k \times$ Median from P

(d) $k \times$ Perimeter of $\triangle \text{PQR}$

(e) $k \times$ Angle bisector of R

(i) Quadrilateral

(ii) Parallelogram

(iii) Trapezium

(iv) Kite

(v) Rectangle

(a) Exactly one pair of parallel sides

(b) A parallelogram with all angles $90^\circ$

(c) Two pairs of adjacent sides are equal

(d) A polygon with 4 sides

(e) Opposite sides are parallel

(i) Rhombus

(ii) Square

(iii) Rectangle

(iv) Parallelogram (general)

(v) Isosceles Trapezium

(a) Diagonals bisect each other

(b) All sides are equal

(c) Non-parallel sides are equal

(d) All angles are $90^\circ$

(e) Both a rectangle and a rhombus

(i) Parallelogram

(ii) Rectangle

(iii) Rhombus

(iv) Square

(v) Kite

(a) Are perpendicular bisectors of each other

(b) Are equal and bisect each other

(c) One diagonal is the perpendicular bisector of the other

(d) Bisect each other

(e) Are equal and perpendicular bisectors of each other

(i) Opposite angles are equal

(ii) All angles are $90^\circ$

(iii) Adjacent angles are supplementary

(iv) Exactly one pair of opposite angles are equal (and the other pair is not)

(v) Two pairs of adjacent angles are equal

(a) Rectangle

(b) Parallelogram

(c) Kite (angles between unequal sides)

(d) Parallelogram

(e) Kite (angles between equal sides)

(i) All four sides are equal

(ii) Opposite sides are equal and parallel

(iii) Exactly one pair of opposite sides is parallel

(iv) Two pairs of adjacent sides are equal

(v) All sides are equal and all angles are $90^\circ$

(a) Trapezium

(b) Square

(c) Rhombus

(d) Parallelogram

(e) Kite

(i) Mid-Point Theorem

(ii) Converse of Mid-Point Theorem

(iii) Property of the line segment joining midpoints

(iv) Application of Mid-Point Theorem in quadrilaterals

(v) Condition for applying the Mid-Point Theorem

(a) Joining the midpoints of two sides of a triangle

(b) A line through the midpoint of one side parallel to another side bisects the third side

(c) The figure formed by joining the midpoints of a quadrilateral is a parallelogram

(d) Is parallel to the third side and half its length

(e) The line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half the length of the third side

(i) DE is related to BC

(ii) $\triangle \text{ADE}$ is related to $\triangle \text{ABC}$

(iii) Perimeter of $\triangle \text{ADE}$ is related to perimeter of $\triangle \text{ABC}$

(iv) Area of $\triangle \text{ADE}$ is related to area of $\triangle \text{ABC}$

(v) Line through D parallel to BC

(a) Half of it

(b) One-fourth of it

(c) Is parallel to BC and half its length

(d) Bisects AC (Converse of MPT)

(e) Is similar to it with ratio 1:2

(i) PQRS is a parallelogram

(ii) PQRS is a rectangle

(iii) PQRS is a rhombus

(iv) PQRS is a square

(v) PQ || AC and PS || BD

(a) AC = BD

(b) Always true (by MPT)

(c) ABCD's diagonals are perpendicular

(d) Always true for any quadrilateral

(e) ABCD's diagonals are equal and perpendicular

(i) Triangle formed by midpoints ($\triangle \text{DEF}$)

(ii) The three quadrilaterals (like ADEF)

(iii) The four smaller triangles formed by joining midpoints

(iv) Each side of the inner triangle (like DE)

(v) The perimeter of the inner triangle ($\triangle \text{DEF}$)

(a) Half the perimeter of the original triangle

(b) Half the length of the corresponding side of the original triangle

(c) Are all congruent to each other

(d) Are parallelograms

(e) Is similar to the original triangle

(i) Midpoints of sides of a triangle

(ii) Line parallel to one side of a triangle

(iii) Ratio of areas of similar triangles

(iv) Sides of a right triangle

(v) Opposite angles of a cyclic quadrilateral

(a) Pythagorean Theorem

(b) Mid-Point Theorem

(c) Sum to $180^\circ$

(d) Basic Proportionality Theorem

(e) Equals the square of the ratio of sides

(i) Area

(ii) Polygonal region

(iii) Figures equal in area

(iv) Unit of area

(v) Base of a figure (for area calculation)

(a) A standard square (like $1 \text{ cm}^2$)

(b) The measure of the region enclosed by a boundary

(c) Figures that enclose the same amount of surface

(d) A side or segment on which the figure rests or from which height is measured

(e) The plane region enclosed by a polygon

(i) Two congruent figures

(ii) Two parallelograms on the same base and between the same parallels

(iii) Two triangles on the same base and between the same parallels

(iv) A triangle and a parallelogram on the same base and between the same parallels

(v) Two figures with the same base and height

(a) Area of triangle is half the area of parallelogram

(b) They have equal area

(c) They have equal area

(d) They have equal area

(e) They are equal in area

(i) Area($\triangle \text{ABD}$)

(ii) Area($\triangle \text{ACD}$)

(iii) $\triangle \text{ABD}$ and $\triangle \text{ACD}$

(iv) Area($\triangle \text{ABD}$) + Area($\triangle \text{ACD}$)

(v) Base BD and CD

(a) Have equal lengths

(b) Equal in area

(c) Half of Area($\triangle \text{ABC}$)

(d) Area($\triangle \text{ABC}$)

(e) Equal to Area($\triangle \text{ACD}$)

(i) Figures on the same base and between the same parallels

(ii) Two triangles with equal area and the same base

(iii) A diagonal of a parallelogram

(iv) A median of a triangle

(v) Area addition postulate

(a) Divides it into two triangles of equal area

(b) Divides it into two congruent triangles

(c) Their vertices opposite the base lie on a line parallel to the base

(d) Their areas are equal

(e) The area of a region is the sum of the areas of its non-overlapping parts

(i) 1 square metre ($\text{m}^2$)

(ii) 1 square centimetre ($\text{cm}^2$)

(iii) 1 hectare

(iv) 1 acre (approx)

(v) 1 square kilometre ($\text{km}^2$)

(a) $10000 \text{ m}^2$

(b) $100 \times 100 \text{ cm}^2$ or $10000 \text{ cm}^2$

(c) $100 \text{ hectares}$

(d) $100 \times 100 \text{ m}^2$

(e) Approximately $4047 \text{ m}^2$

(i) Centre

(ii) Radius

(iii) Diameter

(iv) Circumference

(v) Chord

(a) The distance around the circle

(b) A line segment joining any two points on the circle

(c) A line segment from the centre to any point on the circle

(d) The fixed point from which all points on the circle are equidistant

(e) A chord that passes through the centre

(i) Arc

(ii) Sector

(iii) Segment

(iv) Semicircle

(v) Tangent

(a) The region bounded by a chord and an arc

(b) A line that intersects the circle at exactly one point

(c) An arc whose endpoints are the ends of a diameter

(d) A part of the circumference

(e) The region bounded by two radii and an arc

(i) Longest chord

(ii) Connects centre to circumference

(iii) Ratio of circumference to diameter

(iv) Region between a chord and arc

(v) Line intersecting at two points

(a) Radius

(b) $\pi$

(c) Diameter

(d) Segment

(e) Secant

(i) Centre

(ii) Point on circumference

(iii) Point inside circle (not centre)

(iv) Point outside circle

(v) Endpoint of radius (not centre)

(a) In the exterior

(b) In the interior

(c) On the boundary

(d) In the interior

(e) On the boundary

(i) Have the same radius

(ii) Have different radii

(iii) Have the same centre and same radius

(iv) Have the same centre but different radii

(v) Can be scaled to match each other

(a) Are congruent

(b) Are concentric (but not congruent)

(c) Are similar

(d) Are identical

(e) Are similar but not congruent

(i) Angle at Centre Theorem

(ii) Angles in the Same Segment

(iii) Angle in a Semicircle

(iv) Perpendicular from Centre to Chord

(v) Equal Chords

(a) Are equidistant from the centre

(b) Is a right angle

(c) Is twice the angle at the circumference subtended by the same arc/chord

(d) Are equal

(e) Bisects the chord

(i) Angle subtended by a chord at the centre

(ii) Angle subtended by the same chord on the circumference (major arc)

(iii) Angle in a semicircle

(iv) Angle subtended by a diameter at the circumference

(v) Angles subtended by equal chords at the centre

(a) $90^\circ$

(b) Half the angle at the centre

(c) Equal

(d) $90^\circ$

(e) Twice the angle at the circumference

(i) Chord AB = Chord CD

(ii) Distance of chord AB from O = Distance of chord CD from O

(iii) OM $\perp$ AB, where M is on AB

(iv) M is the midpoint of chord AB

(v) Angle subtended by arc AB at O = Angle subtended by arc CD at O

(a) OM bisects AB

(b) Chord AB = Chord CD

(c) OM $\perp$ AB

(d) Chord AB = Chord CD

(e) Distance of chord AB from O = Distance of chord CD from O

(i) Angle subtended by a chord at the centre is $180^\circ$

(ii) Angle in a segment is obtuse

(iii) Angle in a segment is acute

(iv) Two angles subtended by the same chord are equal

(v) The angle subtended by a chord at the centre is $90^\circ$

(a) The chord subtends an angle of $45^\circ$ on the remaining part of the circle

(b) The chord is a diameter

(c) They are in the same segment

(d) The segment is minor

(e) The segment is major

(i) Finding the centre of a circle

(ii) Drawing a unique circle through three non-collinear points

(iii) Checking if a triangle inscribed in a circle is right-angled

(iv) Proving chords equidistant from center are equal

(v) Proving angle at center is twice angle at circumference

(a) Angle in a Semicircle theorem (if one side is diameter)

(b) Converse of the equidistant chords property

(c) The perpendicular bisectors of any two chords intersect at the center

(d) Angle at Centre Theorem

(e) The perpendicular bisectors of the sides of the triangle are the perpendicular bisectors of chords of the circle passing through vertices

(i) Cyclic quadrilateral

(ii) Concyclic points

(iii) Circumscribed circle

(iv) Exterior angle of a cyclic quadrilateral

(v) Interior opposite angle

(a) Points that lie on the same circle

(b) A quadrilateral whose all vertices lie on a circle

(c) The angle formed by extending a side of the quadrilateral

(d) The circle passing through all the vertices of a polygon

(e) The interior angle opposite to the exterior angle at a vertex

(i) Sum of opposite angles

(ii) Exterior angle at a vertex

(iii) Condition for a quadrilateral to be cyclic

(iv) Any rectangle

(v) Any parallelogram

(a) Sum of opposite angles is $180^\circ$

(b) Is equal to the interior opposite angle

(c) Is always cyclic

(d) $180^\circ$

(e) Is cyclic only if it is a rectangle or square

(i) $\angle A = 70^\circ$

(ii) $\angle B = 110^\circ$

(iii) $\angle C = 80^\circ$

(iv) $\angle D = 95^\circ$

(v) Exterior angle at A $= 100^\circ$

(a) $\angle B = 85^\circ$ (interior opposite)

(b) $\angle D = 70^\circ$

(c) $\angle C = 110^\circ$

(d) $\angle A = 100^\circ$

(e) $\angle C = 100^\circ$

(i) Any square

(ii) Any rhombus

(iii) Any trapezium

(iv) Any isosceles trapezium

(v) Any kite

(a) Can be cyclic only if it's a square

(b) Can be cyclic

(c) Is always cyclic

(d) Can be cyclic only if angles between unequal sides are equal

(e) Can be cyclic only if it is a right trapezium or isosceles trapezium

(i) If sum of opposite angles is $180^\circ$, the quadrilateral is cyclic

(ii) All vertices of a cyclic quadrilateral lie on the same circle

(iii) Exterior angle equals interior opposite angle

(iv) A quadrilateral with one pair of opposite angles supplementary is cyclic

(v) A quadrilateral with all sides equal is always cyclic

(a) True

(b) True

(c) False (e.g., a rhombus)

(d) True

(e) True

(i) Tangent

(ii) Secant

(iii) Point of contact

(iv) Chord

(v) Radius at point of contact

(a) A line segment joining two points on the circle

(b) The point where a tangent touches the circle

(c) A line that intersects the circle at exactly one point

(d) A line that intersects the circle at two distinct points

(e) A line segment from the centre to the point where a tangent touches the circle

(i) Point inside the circle

(ii) Point on the circle

(iii) Point outside the circle

(iv) Centre of the circle

(v) Any point on a tangent (not the point of contact)

(a) One

(b) Zero

(c) Two

(d) Zero (tangents are from a point *to* the circle)

(e) The tangent itself is a line, not drawn *from* a point *to* the circle in this context

(i) Tangent at A is perpendicular to radius OA

(ii) Lengths of tangents from external point P to A and B are equal

(iii) Two parallel tangents to a circle

(iv) A line perpendicular to radius OA at A

(v) Angle between tangent and chord through point of contact

(a) PO bisects $\angle APB$ and $\angle AOB$ (where O is center)

(b) Forms a right angle

(c) The segment joining points of contact is a diameter

(d) Is the tangent at A

(e) Equal to angle in alternate segment

(i) Circles touch externally

(ii) Circles touch internally ($r_1 > r_2$)

(iii) Circles are concentric

(iv) Circles intersect at two distinct points

(v) One circle is completely inside the other without touching

(a) $d < |r_1 - r_2|$

(b) $d = 0$

(c) $|r_1 - r_2| < d < r_1 + r_2$

(d) $d = r_1 + r_2$

(e) $d = r_1 - r_2$

(i) Tangent-Radius Theorem

(ii) Length of Tangents from External Point Theorem

(iii) Alternate Segment Theorem

(iv) Tangent-Secant Theorem (Power of a point)

(v) Secant

(a) Relates the angle between a tangent and a chord to an angle in the circle

(b) Describes the relationship between a radius and a tangent at the point of contact

(c) States that tangent segments from the same external point are equal

(d) Relates the lengths of segments formed by a tangent and a secant from an external point

(e) A line that cuts the circle at two points

(i) Symmetry

(ii) Line symmetry

(iii) Axis of symmetry

(iv) Reflection

(v) Isometry

(a) A transformation that preserves distance

(b) A transformation that flips a figure across a line

(c) A property of a figure where it remains unchanged after a transformation (like reflection or rotation)

(d) Symmetry involving reflection across a line

(e) The line across which a figure is reflected to produce line symmetry

(i) Square

(ii) Rectangle (not a square)

(iii) Equilateral triangle

(iv) Circle

(v) Parallelogram (not a rhombus or rectangle)

(a) 3

(b) 0

(c) Infinite

(d) 4

(e) 2

(i) A

(ii) B

(iii) H

(iv) S

(v) Z

(a) Horizontal only

(b) No line symmetry

(c) Vertical only

(d) Both horizontal and vertical

(e) Rotational symmetry (but not line symmetry)

(i) Reflection across x-axis

(ii) Reflection across y-axis

(iii) Reflection across the line y = x

(iv) Reflection across the origin (equivalent to $180^\circ$ rotation)

(v) Reflection across the line y = -x

(a) (-x, -y)

(b) (y, x)

(c) (x, -y)

(d) (-y, -x)

(e) (-x, y)

(i) Square

(ii) Equilateral Triangle

(iii) Rectangle (not square)

(iv) Parallelogram (not rhombus/rectangle)

(v) Circle

(a) Both line and rotational symmetry

(b) Both line and rotational symmetry

(c) Both line and rotational symmetry (infinite order)

(d) Rotational symmetry only (order 2)

(e) Both line and rotational symmetry

(i) Rotational symmetry

(ii) Centre of rotation

(iii) Angle of rotational symmetry

(iv) Order of rotational symmetry

(v) Trivial rotational symmetry

(a) The smallest angle of rotation (> $0^\circ$) that maps the figure onto itself

(b) The fixed point around which a rotation occurs

(c) A figure coincides with itself after a rotation less than $360^\circ$

(d) The number of times a figure coincides with itself in a $360^\circ$ rotation

(e) A figure only coincides with itself after a $360^\circ$ rotation (order 1)

(i) Equilateral triangle

(ii) Square

(iii) Regular pentagon

(iv) Circle

(v) Parallelogram (not rhombus/rectangle)

(a) 5

(b) 4

(c) Infinite

(d) 3

(e) 2

(i) n = 1

(ii) n = 2

(iii) n = 3

(iv) n = 4

(v) n = 6 (Regular hexagon)

(a) $120^\circ$

(b) $360^\circ$

(c) $60^\circ$

(d) $90^\circ$

(e) $180^\circ$

(i) A

(ii) O

(iii) S

(iv) H

(v) Z

(a) 2

(b) 1

(c) Infinite

(d) 2

(e) 2

(i) Scalene triangle

(ii) Isosceles triangle (not equilateral)

(iii) Rhombus (not square)

(iv) Kite (not rhombus)

(v) Rectangle (not square)

(a) Line symmetry only

(b) No rotational symmetry (order 1), no line symmetry

(c) Both line symmetry and rotational symmetry (order 2)

(d) Rotational symmetry only (order 2)

(e) Line symmetry only

(i) 2-Dimensional shape

(ii) 3-Dimensional shape

(iii) Point

(iv) Line

(v) Plane

(a) 0 dimensions

(b) Length, Breadth, Height (Volume)

(c) Length only (or length and breadth for curves)

(d) Length and Breadth (Area)

(e) 1 dimension

(i) Cube

(ii) Cuboid

(iii) Sphere

(iv) Cylinder

(v) Cone

(a) One circular base and one curved surface

(b) Six square faces

(c) Six rectangular faces

(d) Two circular bases and one curved surface

(e) One curved surface (no flat faces)

(i) Cube

(ii) Triangular Prism

(iii) Square Pyramid

(iv) Sphere

(v) Cone

(a) 0

(b) 6

(c) 1

(d) 8

(e) 5

(i) Cube

(ii) Triangular Prism

(iii) Square Pyramid

(iv) Cylinder

(v) Sphere

(a) 9

(b) 0

(c) 2 (curved edges)

(d) 12

(e) 8

(i) Face

(ii) Edge

(iii) Vertex

(iv) Polyhedron

(v) Curved surface

(a) The flat or curved outer boundary of a solid

(b) A solid bounded by plane faces (polygons)

(c) The intersection of two faces

(d) The intersection of edges

(e) A surface that is not flat (like on a sphere, cylinder, cone)

(i) Oblique sketch

(ii) Isometric sketch

(iii) Orthographic projection

(iv) Cross-section

(v) Net

(a) A 2D pattern that folds to form a 3D solid

(b) Shows Front, Side, and Top views

(c) A 2D shape obtained by slicing a solid with a plane

(d) Front face in true shape, depth at an angle

(e) Uses an isometric grid, edges along axes at $120^\circ$ apparent angles

(i) Cube (horizontal slice)

(ii) Cylinder (parallel to base)

(iii) Cone (vertical slice through apex)

(iv) Sphere (any slice)

(v) Square pyramid (parallel to base)

(a) Circle

(b) Square

(c) Triangle

(d) Circle

(e) Square (similar to base)

(i) Front View

(ii) Side View

(iii) Top View

(iv) Bottom View

(v) Orthographic Projection

(a) Looking from above

(b) Looking from below

(c) Looking from the front

(d) A set of views showing the object from mutually perpendicular directions

(e) Looking from the side

(i) Oblique sketch property

(ii) Isometric sketch property

(iii) Orthographic views property

(iv) Cross-section purpose

(v) Net purpose

(a) Helps understand interior structure

(b) Parallel lines are shown as parallel

(c) Used to construct the solid shape

(d) Front face is true shape

(e) True lengths along isometric axes

(i) Rectangular Prism (Cuboid)

(ii) Triangular Prism

(iii) Cone

(iv) Sphere

(v) Cube

(a) Vertical slice through apex is a triangle

(b) Horizontal slice is a square/rectangle

(c) Any plane slice is a circle

(d) Top view is a rectangle/square

(e) Vertical slice can be a rectangle

(i) Polyhedron

(ii) Face

(iii) Edge

(iv) Vertex

(v) Convex polyhedron

(a) The intersection of edges

(b) A solid bounded by plane faces

(c) A polygonal region forming the boundary of a polyhedron

(d) The intersection of two faces

(e) For any face, the polyhedron lies entirely on one side of its plane

(i) Tetrahedron

(ii) Hexahedron (Cube)

(iii) Octahedron

(iv) Dodecahedron

(v) Icosahedron

(a) Squares

(b) Equilateral triangles

(c) Pentagons

(d) Equilateral triangles

(e) Pentagons

(i) Tetrahedron

(ii) Cube

(iii) Octahedron

(iv) Square Pyramid

(v) Triangular Prism

(a) 6

(b) 8

(c) 5

(d) 4

(e) 5

(i) Tetrahedron

(ii) Cube

(iii) Octahedron

(iv) Square Pyramid

(v) Triangular Prism

(a) 6

(b) 8

(c) 5

(d) 4

(e) 5

(i) Tetrahedron

(ii) Cube

(iii) Octahedron

(iv) Square Pyramid

(v) Triangular Prism

(a) 9

(b) 12

(c) 12

(d) 6

(e) 8