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MCQ Questions for Class 7 Chapter 7 Congruence of Triangles

By Swati Singh

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Updated on 18 Nov 2025, 12:05 IST

Access the CBSE Class 7 Mathematics Congruence of Triangles MCQs (Set B) provided below, available for download in PDF format. These Class 7 Maths MCQs with answers follow the latest syllabus and exam pattern recommended by CBSE, NCERT, and KVS.

Chapter 7 MCQs are essential for exam preparation, helping students strengthen concepts and boost their scores with consistent practice. Explore more chapter-wise MCQs for Class 7 Mathematics and download the latest study materials for all subjects.

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MCQ Questions with Solutions for Class 7 Congruence of Triangles

1. Two figures are said to be congruent when they:

a) Have the same area only
b) Have the same shape only
c) Have the same shape and size
d) Have the same perimeter only
Answer: c
Congruent figures have exactly the same shape and size.

2. Congruent triangles have:

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a) Only equal sides
b) Only equal angles
c) All corresponding sides and angles equal
d) No relation
Answer: c
In congruent triangles, all corresponding sides and angles are equal.

3. Which is a valid criterion for triangle congruence?

a) AAA
b) SSA
c) ASA
d) AAS
Answer: c
ASA (Angle-Side-Angle) is a valid congruence rule.

4. Which of the following is NOT a congruence rule?

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a) SSS
b) SAS
c) ASA
d) SSA
Answer: d
SSA is not a standard congruence rule.

5. In SSS congruence rule, how many sides are compared?

a) 1
b) 2
c) 3
d) 4
Answer: c
SSS compares all three sides of both triangles.

6. If two triangles have two sides and the included angle equal, they are:

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a) SSS
b) SAS
c) ASA
d) AAS
Answer: b
Two sides and the included angle equal is the SAS rule.

7. If ∠A = ∠D, ∠B = ∠E, and AB = DE, which rule applies?

a) SAS
b) ASA
c) SSS
d) AAS
Answer: b
Two angles and the included side equal is ASA.

8. Two right triangles are congruent if:

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a) Their hypotenuse and one side are equal
b) Their angles are equal
c) Their perimeter is same
d) Their area is same
Answer: a
RHS rule: hypotenuse and one side equal in right triangles.

9. Which is a valid right-triangle congruence rule?

a) RHS
b) RAS
c) RSS
d) RAA
Answer: a
RHS stands for Right angle–Hypotenuse–Side.

10. If two triangles are congruent, then their corresponding sides are:

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a) Equal
b) Unequal
c) Always parallel
d) Opposite
Answer: a
Corresponding sides of congruent triangles are equal.

11. If ∠A = ∠X, ∠B = ∠Y, and AC = XZ, which rule proves congruence?

a) SAS
b) AAS
c) AAA
d) SSS
Answer: b
Two angles and a non-included side equal is AAS.

12. If AB = PQ, BC = QR, CA = RP, the triangle congruence is:

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a) SAS
b) ASA
c) SSS
d) RHS
Answer: c
All three sides equal ⇒ SSS congruence.

13. AAA cannot prove congruence because:

a) Angles don’t define shape
b) Sides may be different in size
c) Angles may differ
d) Both a and b
Answer: d
Same angles can give similar but not necessarily congruent triangles.

14. If two triangles are congruent, corresponding angles are:

a) Equal
b) Supplementary
c) Adjacent
d) Perpendicular
Answer: a
All corresponding angles are equal in congruent triangles.

15. Congruent figures are always:

a) Similar
b) Parallel
c) Perpendicular
d) Unequal
Answer: a
Congruent figures are a special case of similar figures (same shape and size).

16. The term “included angle” means:

a) Angle between two sides
b) Largest angle
c) Smallest angle
d) External angle
Answer: a
Included angle is formed by two given sides.

17. Which statement is true?

a) SAS means 2 angles and a side
b) SSS means 3 angles
c) ASA means 2 angles and included side
d) AAS is invalid
Answer: c
ASA = Angle–Side–Angle (the side is between the two angles).

18. RHS stands for:

a) Right-angle, hypotenuse, side
b) Right-angle, height, side
c) Ratio, hypotenuse, side
d) Right-angle, hypotenuse, segment
Answer: a
RHS is used for right triangle congruence.

19. Two triangles having two angles and a non-included side equal are congruent by:

a) ASA
b) SAS
c) AAS
d) SSS
Answer: c
This is the AAS (Angle–Angle–Side) rule.

20. A mirror image of a triangle is:

a) Not congruent
b) Congruent
c) Always larger
d) Not a triangle
Answer: b
A mirror image has same shape and size, so it is congruent.

21. To prove triangles congruent by SAS, which must be equal?

a) 2 angles, 1 side
b) 3 sides
c) 2 sides, included angle
d) 1 side, 1 angle
Answer: c
SAS uses two sides and the angle between them.

22. If ∠ABC = ∠PQR and sides AB = PQ, BC = QR, then triangles are congruent by:

a) ASA
b) SAS
c) SSS
d) AAS
Answer: b
Two sides and included angle equal ⇒ SAS rule.

23. Corresponding parts of congruent triangles are:

a) Opposite
b) Same only sometimes
c) Equal
d) Different
Answer: c
CPCTC: Corresponding Parts of Congruent Triangles are Congruent.

24. AAS rule compares how many angles?

a) 1
b) 2
c) 3
d) 0
Answer: b
AAS uses two angles and one side.

25. Which pair of triangles is congruent?

a) Side ratios equal
b) Areas equal
c) All three sides equal
d) All angles equal
Answer: c
Equal corresponding sides (SSS) guarantee congruence.

26. RHS rule applies when:

a) A triangle is acute
b) A triangle is obtuse
c) A triangle is right-angled
d) A triangle is equilateral
Answer: c
RHS is only for right-angled triangles.

27. Two triangles with same perimeter are:

a) Always congruent
b) Never congruent
c) Sometimes congruent
d) Impossible
Answer: c
Same perimeter does not guarantee congruence, but they can be congruent in some cases.

28. “CPCTC” stands for:

a) Corresponding parts of congruent triangles are congruent
b) Corresponding points of common triangles are central
c) Central parts of congruent triangles are common
d) None
Answer: a
CPCTC is a key result used after proving triangles congruent.

29. If two sides and non-included angle are equal, the rule is:

a) SAS
b) AAS
c) SSS
d) RHS
Answer: b
Two angles and a side (not between them) is AAS.

30. Which rule is best for proving congruence in right triangles?

a) SAS
b) RHS
c) SSS
d) AAA
Answer: b
RHS is specifically designed for right triangles.

31. If ΔABC ≅ ΔPQR, then ∠B corresponds to:

a) ∠P
b) ∠Q
c) ∠R
d) None
Answer: b
Order of letters shows correspondence: A ↔ P, B ↔ Q, C ↔ R.

32. Two congruent triangles have equal:

a) Only bases
b) Only heights
c) All corresponding sides and angles
d) Only one angle
Answer: c
All corresponding parts are equal for congruent triangles.

33. If two triangles have equal hypotenuse and equal one side but no right angle, then:

a) RHS applies
b) SAS applies
c) No rule applies
d) AAA applies
Answer: c
RHS requires the triangles to be right-angled; without right angle, RHS cannot be used.

34. Congruence symbol is:

a) ≈
b) =
c) ≅
d) ∞
Answer: c
The symbol “≅” is used to denote congruence.

35. Which rule is based on three sides only?

a) SAS
b) ASA
c) SSS
d) AAS
Answer: c
SSS uses only side lengths of the triangles.

 

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MCQ Questions for Class 7 Chapter 7 FAQs

What does “congruence” mean in triangles?

Congruence means two triangles have exactly the same shape and size. This happens when all corresponding sides and angles are equal.

How do we check if two triangles are congruent?

You can use rules like SSS, SAS, ASA, and RHS to determine if two triangles are congruent.

What is the SSS rule?

SSS (Side-Side-Side) states that if all three sides of one triangle match the three sides of another triangle, the triangles are congruent.

What is the difference between congruent and similar triangles?

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.

Why is congruence important in geometry?

It helps in proving shapes identical, solving geometric problems, and understanding properties of figures.

What is the RHS congruence rule?

RHS (Right angle–Hypotenuse–Side) states that two right-angled triangles are congruent if their hypotenuse and one corresponding side are equal.

Do congruent triangles always have equal area?

Yes. Since their sides and angles are identical, their area is also the same.

Is the AAA rule used for congruence?

No. AAA only shows similarity, not congruence, because size may differ.