How many practice questions are available for Congruence & Symmetry?

SparkEd Math offers 60+ practice questions for Congruence & Symmetry across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Congruence & Symmetry content free on SparkEd Math?

Yes! All Congruence & Symmetry content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Congruence & Symmetry differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Congruence & Symmetry problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Congruence & Symmetry content aligned with the CBSE syllabus?

Yes, all Congruence & Symmetry questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 7. The content follows the official curriculum structure and exam pattern.

Congruence & Symmetry — Class 7 CBSE (2025-26)

About Congruence & Symmetry — Class 7 CBSE

Identify congruent figures and explore rotational and reflective symmetry. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 9). On this page you can practice 61 questions across three difficulty levels — 20 easy, 21 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 36-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Congruence & Symmetry

Introduction to Congruence: Same Size, Same Shape
Congruence of Geometric Figures: Segments, Angles, and Triangles
Criteria for Congruence of Triangles
Understanding Symmetry: Line and Rotational
Transformations, Connections, and Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Congruence & Symmetry — solved examples for Class 7 CBSE

Example 1easy

Which of the following best defines what it means for two geometric figures to be congruent?

A)A) They have the same shape and the same size, meaning one can be perfectly superimposed on the other.
B)B) They have the same shape but may have different sizes.
C)C) They have the same size but may have different shapes.
D)D) They are mirror images of each other, but not necessarily identical.

Step-by-step solution

The definition of congruence in geometry means that two figures are exactly alike.
This implies they must have both the same shape and the same size.
If one figure can be moved (translated, rotated, reflected) and perfectly overlap the other, they are congruent. Option A provides the most complete and accurate definition.

Answer: A) They have the same shape and the same size, meaning one can be perfectly superimposed on the other.

Example 2medium

Consider two figures, Figure P and Figure Q. If Figure P is congruent to Figure Q, which of the following statements must be true?

A)Figure P has the same area as Figure Q but a different perimeter.
B)Figure P can be perfectly superimposed on Figure Q by a series of rigid transformations.
C)Figure P is similar to Figure Q but not necessarily the same size.
D)Figure P has the same number of sides as Figure Q, but their corresponding angles might be different.

Step-by-step solution

Congruent figures are figures that have the exact same shape and the exact same size. They are identical in all respects.
This means that one figure can be perfectly placed on top of the other, coinciding exactly. This superimposition is achieved through rigid transformations (translation, rotation, reflection) which preserve size and shape.
Option A is incorrect because congruent figures must have both the same area and the same perimeter. Option C describes similarity, not congruence. Option D is incorrect because corresponding angles must also be equal for congruence.

Answer: Figure P can be perfectly superimposed on Figure Q by a series of rigid transformations.

Example 3hard

Which of the following statements *must always* be true for two figures to be congruent?

A)They have the same area.
B)They have the same perimeter.
C)They can be perfectly superimposed on each other.
D)They are made of the same material.

Step-by-step solution

Congruent figures are defined as figures that have exactly the same shape and the same size.
If two figures have the same shape and size, they can be placed one over the other to perfectly cover each other without any part sticking out. This is called superimposition.
Figures can have the same area (e.g., a square and a rectangle) or perimeter (e.g., a rectangle and a triangle) without being congruent. The material they are made of is irrelevant to their geometric congruence.

Answer: They can be perfectly superimposed on each other.

Practice questions on Congruence & Symmetry

Q1.easy
Two line segments are congruent if and only if:
1. A)A) They are parallel to each other.
2. B)B) They have the same length.
3. C)C) They are perpendicular to each other.
4. D)D) They lie on the same line.
Show answer
Answer: B) They have the same length.
Hint: For line segments, what is the only property that determines their 'size'?
Q2.easy
When are two angles, say ∠ABC and ∠PQR, considered congruent?
1. A)A) When their arms are of the same length.
2. B)B) When they have the same vertex.
3. C)C) When their measures (in degrees) are equal.
4. D)D) When they are vertically opposite angles.
Show answer
Answer: C) When their measures (in degrees) are equal.
Hint: The size of an angle is determined by its measure, not the length of its arms.
Q3.easy
Consider two triangles, ΔABC and ΔXYZ. If AB = XY, BC = YZ, and CA = ZX, which congruence criterion applies?
1. A)A) SAS (Side-Angle-Side)
2. B)B) ASA (Angle-Side-Angle)
3. C)C) SSS (Side-Side-Side)
4. D)D) RHS (Right angle-Hypotenuse-Side)
Show answer
Answer: C) SSS (Side-Side-Side)
Hint: Look at what information is given about the triangles – are they sides or angles?
Q4.medium
In a rhombus ABCD, the diagonal AC is drawn. If AB = 5 cm, BC = 5 cm, CD = 5 cm, and DA = 5 cm, and angle ABC = 70°, can we conclude that triangle ABC is congruent to triangle ADC? If so, by which criterion?
1. A)Yes, by SSS criterion.
2. B)Yes, by SAS criterion.
3. C)No, because we don't know the length of AC.
4. D)No, because a rhombus does not guarantee congruent triangles by any standard criterion.
Show answer
Answer: Yes, by SSS criterion.
Hint: Remember the properties of a rhombus and what information is needed for the SSS congruence criterion.
Q5.medium
Two triangles, ΔPQR and ΔXYZ, are being examined for congruence. You are given that PQ = XY and PR = XZ. To prove that ΔPQR ≅ ΔXYZ using the SAS (Side-Angle-Side) criterion, what additional information is absolutely necessary?
1. A)QR = YZ
2. B)∠P = ∠X
3. C)∠Q = ∠Y
4. D)∠R = ∠Z
Show answer
Answer: ∠P = ∠X
Hint: For the SAS criterion, the angle must be 'included' between the two given sides. Which angle is included between sides PQ and PR?
Q6.medium
In two triangles, ΔABC and ΔDEF, you are given that ∠A = 60°, ∠B = 80°, and side AB = 5 cm. In ΔDEF, you know that ∠D = 60°, ∠F = 40°, and side DF = 5 cm. Are these triangles congruent? If so, by which criterion?
1. A)Yes, by ASA criterion.
2. B)Yes, by SAS criterion.
3. C)No, they are not congruent.
4. D)Yes, by AAS criterion (Angle-Angle-Side).
Show answer
Answer: Yes, by ASA criterion.
Hint: For ASA, you need two angles and the *included side*. If the included side isn't directly given, can you find a missing angle first?
Q7.hard
In triangle PQR, PQ = PR. PS is the angle bisector of ∠P, meeting QR at S. If ∠QPS = 30°, what is the measure of ∠Q?
1. A)30°
2. B)60°
3. C)75°
4. D)90°
Show answer
Answer: 60°
Hint: In an isosceles triangle, the angle bisector of the vertex angle has special properties.
Q8.hard
Two triangles, ΔABC and ΔDBC, are drawn on the same base BC. If AB = DC and AC = DB, which congruence criterion proves ΔABC ≅ ΔDCB?
1. A)SAS
2. B)ASA
3. C)SSS
4. D)RHS
Show answer
Answer: SSS
Hint: Look for common sides, even if not explicitly stated as equal.
Q9.hard
Rohan wants to prove ΔPQR ≅ ΔXYZ. He has the following information: PQ = XY, PR = XZ, and ∠Q = ∠Y. Which of the following statements is true regarding his approach?
1. A)He can prove congruence using SAS.
2. B)He cannot prove congruence using SAS because ∠Q is not the included angle.
3. C)He can prove congruence using ASA.
4. D)He can prove congruence using SSS.
Show answer
Answer: He cannot prove congruence using SAS because ∠Q is not the included angle.
Hint: For SAS congruence, the angle must be *between* the two given sides.

These are 9 of the 61 questions available for Congruence & Symmetry. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.