Are these practice questions for Geometric Twins based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 7 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Geometric Twins free?

Yes. Every chapter includes free practice questions for Class 7 students to get you started.

What types of questions are included?

The practice set for Geometric Twins mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Geometric Twins for full coverage.

How many practice questions are there for Geometric Twins?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Geometric Twins Class 7 Mathematics Practice Questions with Answers

easy

If it is given that

\triangle XYZ \cong \triangle PQR

, name the angle that corresponds to

\angle Z

.

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easy

Define the term 'congruent figures' in geometry.

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easy

Explain the SSS (Side-Side-Side) congruence condition for two triangles.

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easy

In the given figure,

PS

is a line segment and

Q

is a point such that

PQ = QS

.

R

is another point such that

PR = SR

and

\angle PQR = \angle SQR

. Demonstrate that

\triangle PQR \cong \triangle SQR

.

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easy

If two circles are stated to be congruent, what can you say about their radii? Explain your reasoning.

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easy

In the given figure, O is the midpoint of both line segments

PQ

and

RS

. Analyze the triangles

\triangle POR

and

\triangle QOS

to determine if they are congruent. If they are, state the congruence criterion used.

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easy

It is given that

\triangle PQR \cong \triangle XYZ

. List all the pairs of corresponding vertices, sides, and angles.

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easy

Explain the SSS (Side-Side-Side) congruence condition in your own words.

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easy

In

\triangle PQR

and

\triangle STU

, it is given that

PQ = ST

,

QR = TU

, and

PR = SU

. Analyze the given information and identify the congruence criterion that proves

\triangle PQR \cong \triangle STU

.

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easy

In

\triangle ABC

, the angle at vertex B is

90^\circ

. Identify the hypotenuse and the two sides that form the right angle.

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easy

Critique the statement: "Any two equilateral triangles are congruent."

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easy

Examine the RHS congruence criterion. What specific type of triangle must be involved for this criterion to be applicable?

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easy

Name the congruence condition where two angles and a non-included side of one triangle are equal to the corresponding angles and side of another triangle.

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easy

Justify why knowing only the three angles of two triangles (AAA) is not sufficient to prove their congruence.

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easy

Define what is meant by 'congruent figures' in geometry.

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easy

If it is established that

\triangle DEF \cong \triangle GHI

, apply the concept of corresponding parts to determine which angle in

\triangle GHI

is equal to

\angle FDE

.

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easy

Examine the figure where

\angle DBC = \angle EBC

and

\angle DCB = \angle ECB

. Demonstrate that

\triangle DBC \cong \triangle EBC

and conclude that

CD = CE

.

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easy

If it is given that

\triangle ABC \cong \triangle FDE

, examine the correspondence and identify the side in

\triangle FDE

that is equal to side

AC

.

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easy

In

\triangle PQR

and

\triangle STU

, it is given that

PQ = ST

,

QR = TU

, and

PR = SU

. Analyze the given information and identify the congruence criterion that can be used to prove that

\triangle PQR \cong \triangle STU

.

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easy

Design a proof to show that in a parallelogram

ABCD

, the diagonal

AC

divides it into two congruent triangles.

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easy

What is the measure of each interior angle in an equilateral triangle?

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easy

Name the specific congruence condition that applies only to right-angled triangles.

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easy

A student claims that if quadrilateral ABCD is a kite with

AB=AD

and

CB=CD

, then

\triangle ABC \cong \triangle ADC

. Justify this claim.

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easy

What do the letters in the 'SAS' congruence criterion stand for?

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medium

Design a step-by-step geometric construction method to create a triangle

\triangle PQR

that is congruent to a given triangle

\triangle ABC

, using only a compass and a straightedge, based on the SAS criterion. Justify why your construction guarantees congruence.

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medium

Two triangles are drawn with their corresponding angles equal. Analyze if this is a sufficient condition for the triangles to be congruent. Provide a reason for your answer.

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medium

In an isosceles triangle

\triangle PQR

, the lengths of side

PQ

and side

PR

are equal. Identify which two angles in the triangle must also be equal and state the geometric property that confirms this.

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medium

Two triangles,

\triangle ABC

and

\triangle PQR

, have the following measurements:

\angle A = \angle P = 50^\circ

,

\angle B = \angle Q = 70^\circ

, and

AC = PR = 6

cm. Examine if the triangles are congruent. If yes, state the criterion.

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medium

Examine the two triangles shown below. Given that

AC = DC

and

BC = EC

. Which congruence criterion can be used to demonstrate that

\triangle ABC \cong \triangle DEC

?

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medium

To prove that two right-angled triangles are congruent using the RHS criterion, what three conditions must you demonstrate to be true?

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medium

In quadrilateral

ABCD

, it is given that

AB = AD

and

CB = CD

. Demonstrate that

\triangle ABC \cong \triangle ADC

. Also, determine if diagonal

AC

bisects

\angle BCD

.

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medium

Given a line segment

AB

.

C

is a point such that

CA = CB

. A perpendicular is drawn from

C

to

AB

, meeting at point

M

. Analyze

\triangle AMC

and

\triangle BMC

to prove they are congruent. Which criterion applies?

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medium

List and explain three of the five conditions that guarantee two triangles are congruent. For each condition, provide a simple description.

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medium

In an isosceles triangle

\triangle ABC

with

AB=AC

, the bisectors of

\angle B

and

\angle C

intersect at point

O

. Design a proof to show that

\triangle OBC

is also an isosceles triangle.

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medium

Propose the minimum set of measurements required to create a unique triangle that is congruent to a given equilateral triangle of side length 5 cm, and justify your choice.

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medium

To prove

\triangle ABC \cong \triangle PQR

using the ASA criterion, you are given that

\angle B = \angle Q

and

\angle C = \angle R

. Justify which pair of sides must be equal for this criterion to apply.

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medium

Formulate a proof that the diagonals of a rhombus are perpendicular bisectors of each other.

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medium

Critique the following congruence statement based on the given information: In

\triangle PQR

and

\triangle XYZ

,

PQ=XY

,

QR=YZ

, and

PR=XZ

. A student writes

\triangle PQR \cong \triangle YZX

.

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medium

In a circle with center O, AB is a chord and OM is the perpendicular from the center to the chord. Apply congruence rules to show that the perpendicular from the center bisects the chord (i.e.,

AM = BM

).

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medium

If two squares are congruent, what can you state about the lengths of their sides?

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medium

ABCD is a quadrilateral in which

AD = BC

and

\angle ADC = \angle BCD

. Demonstrate that the diagonals of the quadrilateral are equal, i.e.,

AC = BD

.

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medium

Two triangles,

\triangle XYZ

and

\triangle LMN

, have the following measurements:

XY = LM = 5

cm,

\angle Y = \angle M = 90^\circ

, and

XZ = LN = 13

cm. A student claims they are not congruent because the given information matches the SSA condition. Evaluate the student's claim and provide the correct reasoning.

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medium

In

\triangle LMN

,

LM = LN

and

\angle L = 70^\circ

. Calculate the measure of

\angle M

.

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medium

Given an isosceles triangle

\triangle ABC

with

AB = AC

. If D is the midpoint of the base BC, demonstrate that the altitude from A to BC bisects

\angle BAC

.

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medium

State the full form of the RHS congruence condition.

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medium

Explain the concept of 'corresponding parts' in the context of congruent triangles. If it is given that

\triangle PQR \cong \triangle LMN

, identify and list all six pairs of corresponding parts (three sides and three angles).

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medium

Describe the necessary parts that must be equal for the SAS (Side-Angle-Side) congruence condition to be met. Explain the importance of the angle being 'included'.

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medium

Explain why knowing that all three angles of one triangle are equal to all three angles of another triangle (AAA) is not sufficient to prove congruence.

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medium

In an isosceles triangle

ABC

with

AB = AC

, points

D

and

E

are on side

BC

such that

BD = CE

. Demonstrate that

AD = AE

.

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medium

In

\triangle XYZ

, it is given that the side

XY

is equal to the side

XZ

. Identify the pair of equal angles in this triangle and state the reason for their equality.

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medium

In an isosceles triangle

\triangle PQR

where

PQ = PR

, a point M is the midpoint of the base QR. Formulate a proof to show that the line segment PM is perpendicular to QR.

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medium

List and describe the five main conditions that are sufficient to prove that two triangles are congruent. For each condition, state what each letter represents.

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medium

Explain why knowing that all three angles of two triangles are equal (AAA condition) is not sufficient to state that they are congruent.

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medium

In quadrilateral ABCD, it is given that

AB = AD

and

CB = CD

. Justify that the diagonal AC bisects

\angle BAD

and

\angle BCD

.

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medium

In the given figure, O is the center of the circle, and chord

AB =

chord

CD

. Justify that

\triangle OAB \cong \triangle OCD

. What can you conclude about

\angle AOB

and

\angle COD

?

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medium

Create a quadrilateral

WXYZ

that is not a parallelogram, but in which diagonal

WY

divides it into two congruent triangles. Justify your design.

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medium

If

\triangle LMN \cong \triangle RST

, list the three pairs of corresponding sides and three pairs of corresponding angles that must be equal.

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medium

Describe the minimum measurements you would need to take to check if two given rectangles are congruent.

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medium

A student is given that in

\triangle LMN

and

\triangle XYZ

,

\angle M = \angle Y = 90^\circ

,

LM=XY

, and

LN=XZ

. The student concludes

\triangle LMN \cong \triangle XYZ

by the SAS criterion. Critique this reasoning and provide the correct justification.

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medium

In a circle with center

O

, points

A, B, C, D

are on the circumference such that chord

AB

is equal to chord

CD

. Formulate a proof that

\angle AOB = \angle COD

.

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medium

In the figure, line segments AC and BD bisect each other at point O. Analyze the triangles formed and demonstrate that AB is parallel to DC.

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medium

Evaluate why the SSA (Side-Side-Angle) condition, where the angle is not included between the sides, is not sufficient to prove triangle congruence.

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medium

Recall the property that relates equal sides to angles in an isosceles triangle.

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medium

In a quadrilateral

ACBD

, it is given that

AC=AD

and

BC=BD

. Formulate a proof that line segment

AB

bisects

\angle CAD

.

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medium

In quadrilateral ABCD, it is given that

AB \parallel DC

and

AD \parallel BC

. Apply congruence rules to demonstrate that

\triangle ABD \cong \triangle CDB

.

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medium

A student claims that if two right-angled triangles have their hypotenuse and one other side equal, they are congruent by the SSA condition. Critique this statement.

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hard

Evaluate the following statement and justify your answer: "If two triangles are similar and have the same perimeter, they must be congruent."

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hard

Given an isosceles triangle

\triangle PQR

where

PQ = PR

.

M

is the midpoint of

QR

. Justify that the line segment

PM

is perpendicular to

QR

.

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hard

Analyze the statement: 'If two angles and one side of a triangle are equal to two angles and one side of another triangle, then the two triangles are congruent.' Is this statement always true? Identify the two congruence rules related to this statement.

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hard

ABCD

is a square. A point

P

is inside the square such that

\triangle PDC

is an equilateral triangle. Analyze the figure to calculate the measure of

\angle APB

.

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hard

Two triangles,

\triangle PQR

and

\triangle STU

, are right-angled at Q and T respectively. If hypotenuse

PR = 13

cm, side

QR = 5

cm, hypotenuse

SU = 13

cm and side

ST = 12

cm, calculate the length of side TU and determine if the triangles are congruent.

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hard

Propose the minimum measurements needed to create a unique isosceles triangle and justify your choice.

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hard

In the figure, ABCD is a square and P is a point inside such that

\triangle APD

is an equilateral triangle. Justify that

\triangle APB

is an isosceles triangle and then formulate a proof to find the measure of

\angle APB

.

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hard

In the figure, it is given that

AB

is parallel to

DC

and

AB = DC

. Demonstrate that

AD = BC

.

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hard

You are given two triangles,

\triangle ABC

and

\triangle PQR

, where

AB=PQ

,

\angle B = \angle Q

, and

BC = QR

. A classmate claims this information is sufficient to prove congruence. Now, consider a new pair,

\triangle DEF

and

\triangle STU

, where

DE=ST

,

EF=TU

, and

\angle D = \angle S

. Critique the sufficiency of the information in the second case compared to the first. Propose what change is needed in the second case to guarantee congruence by SAS.

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hard

Evaluate the statement: "Any two rectangles with the same area are congruent." Provide a justification for your evaluation.

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hard

In the given figure, AC = AE, AB = AD and

\angle BAD = \angle EAC

. Demonstrate that

BC = DE

.

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hard

Describe the difference between the SAS (Side-Angle-Side) and SSA (Side-Side-Angle) conditions. Explain why SAS guarantees congruence but SSA does not.

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hard

In the given figure,

AC = AE

,

AB = AD

and

\angle BAD = \angle EAC

. Apply congruence rules to demonstrate that

BC = DE

.

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hard

Identify which congruence condition (SSS, SAS, ASA, or AAS) applies if in

\triangle DEF

and

\triangle LMN

, it is known that

DE = LM

,

\angle E = \angle M

, and

\angle F = \angle N

.

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hard

In

\triangle PQR

, the angle bisector of

\angle P

meets the side

QR

at point

S

. It is also given that

PS

is perpendicular to

QR

. Analyze

\triangle PQS

and

\triangle PRS

and prove that

\triangle PQR

is an isosceles triangle.

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hard

Describe the key differences between the SSS, SAS, and ASA congruence criteria. For each criterion, provide a simple explanation of the parts that need to be equal.

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hard

A student tries to prove that two triangles

\triangle ABC

and

\triangle DEF

are congruent. They are given

AB = DE

,

BC = EF

, and

\angle A = \angle D

. The student concludes congruence by SAS. Critique this conclusion and create a diagram of a counterexample to support your critique.

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hard

Create a word problem based on a real-life scenario where a person must use the ASA congruence criterion to indirectly measure the width of a river. Describe the steps they would take.

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hard

Summarize all the information about corresponding parts that is conveyed by the congruence statement

\triangle BOX \cong \triangle PEN

.

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hard

Explain how the concept of triangle congruence can be used to prove that all three angles of an equilateral triangle are equal to

60^\circ

.

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hard

A textbook provides the following proof to show that in a parallelogram PQRS, the diagonal PR divides it into two congruent triangles. Step 1: In

\triangle PSR

and

\triangle RQP

, we have

PS = QR

(Opposite sides). Step 2:

SR = QP

(Opposite sides). Step 3:

\angle S = \angle Q

(Opposite angles). Step 4: Therefore, by SAS congruence,

\triangle PSR \cong \triangle RQP

. Evaluate this proof. Is it logically sound? If not, identify the flaw and provide a correct proof.

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hard

Formulate a proof that the diagonals of a rhombus bisect each other at right angles. (A rhombus is a quadrilateral with all four sides equal).

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Geometric TwinsClass 7 Mathematics Practice Questions