How many practice questions are available for Congruence?

SparkEd Math offers 60+ practice questions for Congruence 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 content free on SparkEd Math?

Yes! All Congruence 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 differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Congruence 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 content aligned with the ICSE syllabus?

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

Congruence — Class 7 ICSE (2025-26)

About Congruence — Class 7 ICSE

Learn congruence rules for triangles including SSS, SAS, ASA, and RHS criteria. This topic is part of the ICSE Class 7 mathematics syllabus (chapter: Chapter 10). On this page you can practice 59 questions across three difficulty levels — 20 easy, 19 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 34-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Congruence

Introduction to Congruence
Congruence of Triangles: SSS and SAS Criteria
Congruence of Triangles: SAS and ASA Criteria
Congruence of Triangles: ASA, AAS and RHS Criteria
Summary, Connections, and Exam Preparation

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

Congruence — solved examples for Class 7 ICSE

Example 1easy

If two geometric figures are congruent, what can be concluded about them?

A)They have the same shape but different sizes.
B)They have different shapes but the same size.
C)They have the same shape and the same size.
D)They are similar but never equal.

Step-by-step solution

Congruence is a fundamental concept in geometry.
Two figures are said to be congruent if they are exactly the same in terms of shape and size.
This means that one figure can be perfectly superimposed on the other.

Answer: They have the same shape and the same size.

Example 2medium

Triangle ABC has sides AB = 5 cm, BC = 7 cm, CA = 6 cm. Triangle PQR has sides PQ = 7 cm, QR = 6 cm, RP = 5 cm. Are the triangles congruent? If yes, by which criterion?

A)Yes, by SSS
B)Yes, by SAS
C)Yes, by ASA
D)No, they are not congruent

Step-by-step solution

Identify the given side lengths for ΔABC: AB = 5 cm, BC = 7 cm, CA = 6 cm.
Identify the given side lengths for ΔPQR: PQ = 7 cm, QR = 6 cm, RP = 5 cm.
Observe that AB = RP (5 cm), BC = PQ (7 cm), and CA = QR (6 cm). Since all three sides of ΔABC are equal to the three corresponding sides of ΔPQR, the triangles are congruent by the SSS criterion.

Answer: Yes, by SSS

Example 3hard

In the given figure, AD = BC and AC = BD. What congruence criterion proves that ΔABD ≅ ΔBAC, and what is the value of ∠DAB if ∠CBA = 50°?

A)SSS, 50°
B)SAS, 50°
C)ASA, 60°
D)RHS, 40°

Step-by-step solution

Consider ΔABD and ΔBAC:
1. AD = BC (Given)
$AD = BC$
2. BD = AC (Given)
$BD = AC$
3. AB = BA (Common side)
$AB = BA$
Therefore, by SSS (Side-Side-Side) congruence criterion, ΔABD ≅ ΔBAC. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), corresponding angles are equal. So, ∠DAB = ∠CBA. Given ∠CBA = 50°, thus ∠DAB = 50°.

Answer: SSS, 50°

Practice questions on Congruence

Q1.easy
Two line segments are congruent if they have:
1. A)The same length.
2. B)Different lengths.
3. C)The same starting point.
4. D)Parallel alignment.
Show answer
Answer: The same length.
Hint: Think about what makes line segments identical. What measurable property defines a line segment?
Q2.easy
Two angles are congruent if they have:
1. A)The same vertex.
2. B)The same measure.
3. C)The same arm direction.
4. D)Different measures.
Show answer
Answer: The same measure.
Hint: Consider what defines an angle quantitatively. What property determines if two angles are identical?
Q3.easy
If ΔABC ≅ ΔPQR, which side in ΔPQR corresponds to side AB in ΔABC?
1. A)PQ
2. B)QR
3. C)RP
4. D)AC
Show answer
Answer: PQ
Hint: When two triangles are congruent, their corresponding parts are equal. The order of the vertices in the congruence statement matters.
Q4.medium
In triangles XYZ and LMN, it is given that XY = LM = 8 cm, YZ = MN = 6 cm, and ∠Y = ∠M = 70°. Are the triangles congruent? If yes, by which criterion?
1. A)Yes, by SSS
2. B)Yes, by SAS
3. C)Yes, by ASA
4. D)No, they are not congruent
Show answer
Answer: Yes, by SAS
Hint: Check if two sides and the *included* angle of one triangle are equal to the corresponding parts of the other.
Q5.medium
Consider ΔABC and ΔDEF. If ∠B = ∠E = 60°, ∠C = ∠F = 80°, and BC = EF = 9 cm, which congruence criterion applies?
1. A)SSS
2. B)SAS
3. C)ASA
4. D)RHS
Show answer
Answer: ASA
Hint: Look for two angles and the side *between* them.
Q6.medium
In two right-angled triangles, ΔABC (right-angled at B) and ΔPQR (right-angled at Q), it is given that AC = PR = 10 cm and AB = PQ = 6 cm. Which congruence criterion proves ΔABC ≅ ΔPQR?
1. A)SSS
2. B)SAS
3. C)ASA
4. D)RHS
Show answer
Answer: RHS
Hint: This criterion is specifically for right-angled triangles involving the hypotenuse and a side.
Q7.hard
In ΔPQR, PQ = PR and ∠Q = 70°. If S is a point on QR such that PS bisects ∠QPR, which congruence criterion proves ΔPQS ≅ ΔPRS and what is ∠PSR?
1. A)SAS, 90°
2. B)ASA, 90°
3. C)SSS, 70°
4. D)RHS, 110°
Show answer
Answer: SAS, 90°
Hint: First, find all angles in ΔPQR using the isosceles triangle property. Then, use the angle bisector property to find angles within ΔPQS and ΔPRS.
Q8.hard
In ΔABC, AB = AC. P and Q are points on AB and AC respectively, such that PQ is parallel to BC. If BE ⊥ AC and CF ⊥ AB are altitudes from B and C, and BE = CF, which congruence criterion can be used to prove ΔBCE ≅ ΔCBF?
1. A)SSS
2. B)SAS
3. C)ASA
4. D)RHS
Show answer
Answer: RHS
Hint: Focus on the two triangles ΔBCE and ΔCBF. Identify the right angles, the common side, and any other given equal sides to determine the congruence criterion.
Q9.hard
In a parallelogram ABCD, the diagonals AC and BD intersect at O. If AB = 8 cm, BC = 5 cm, and AC = 10 cm, which congruence criterion proves ΔABC ≅ ΔCDA, and what is the length of side CD?
1. A)SAS, 5 cm
2. B)SSS, 8 cm
3. C)ASA, 8 cm
4. D)RHS, 5 cm
Show answer
Answer: SSS, 8 cm
Hint: Recall the properties of a parallelogram, specifically regarding its opposite sides. Then, identify all equal sides in the two triangles, including any common sides.

These are 9 of the 59 questions available for Congruence. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.