Class 7 Mathematics

Chapter 7: Congruence of Triangles

NCERT Textbook Questions & Answers

Question 1

State whether the triangles in each of the following pairs are congruent or not. If they are congruent, state the criterion used.

Answer:

Step 1: Observe the given triangles carefully.

Step 2: Compare the sides and angles of both triangles.

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent by the SSS rule.

If two sides and the included angle of one triangle are equal to those of another triangle, then the triangles are congruent by the SAS rule.

If two angles and the included side of one triangle are equal to those of another triangle, then the triangles are congruent by the ASA rule.

If the triangles are right-angled and their hypotenuse and one side are equal, then they are congruent by the RHS rule.

✅ Conclusion: Use the correct rule based on the given data.

Question 2

Write the congruence rule that can be used to prove that two triangles are congruent when the lengths of all the three sides of one triangle are equal to the corresponding sides of another triangle.

Answer:

Step 1: Given that all three sides of one triangle are equal to the three sides of another triangle.

Step 2: Recall the congruence rules.

When all three corresponding sides of two triangles are equal, the triangles are congruent by the SSS (Side-Side-Side) Congruence Rule.

✅ Final Answer: SSS Congruence Rule

Question 3

Which congruence rule is used to prove that two right-angled triangles are congruent?

Answer:

Step 1: Note that both triangles are right-angled.

Step 2: In right-angled triangles, we compare:

• The right angle
• The hypotenuse
• One corresponding side

If these three are equal in both triangles, then the triangles are congruent.

✅ Final Answer: RHS (Right angle-Hypotenuse-Side) Congruence Rule

Question 4

Are two triangles with equal perimeters always congruent? Give reason.

Answer:

Step 1: Equal perimeters mean only the total length of sides is equal.

Step 2: The individual sides may still be different.

So, triangles can have the same perimeter but different shapes and sizes.

Example:

• Triangle A: sides 3 cm, 4 cm, 5 cm
• Triangle B: sides 2 cm, 5 cm, 5 cm

Both have the same perimeter (12 cm), but their sides are different.

✅ Final Answer: No, triangles with equal perimeters are not always congruent.

Question 5

Which congruence rule states that if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, then the triangles are congruent?

Answer:

Step 1: Identify the given parts:

• Two angles
• The side between the two angles

Step 2: Recall the congruence rules.

This condition matches the ASA Congruence Rule.

✅ Final Answer: ASA Congruence Rule

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Class 7 Mathematics – Chapter 7
NCERT Textbook Questions & Answers

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