To prove △ A M P ≅ △ A M Q , supply the missing reasons in the following proof. Steps Reasons (I) P M = Q M (i) (ii) ∠ P M A ≅ ∠ Q M A (ii) (iii) A M = A M (iii) (iv) △ A M P ≅ △ A M Q (iv)

We need to prove that △ A M P ≅ △ A M Q . Consider △ A M P and △ A M Q , P M = M Q (Corresponding equal sides) ∠ P M A = ∠ Q M A (Corresponding equal angles) A M = A M (Common side) We know that, According to S A S congruence criterion, if two sides and the angle included between the two sides of a triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent. Hence, △ A M P ≅ △ A M Q The required table is shown below. Steps Reasons (i) P M = Q M (i) Corresponding sides (ii) ∠ P M A ≅ ∠ Q M A (ii) Corresponding angles (iii) A M = A M (iii) Common side (iv) △ A M P ≅ △ A M Q (iv) S A S congruence criterion

Complete the congruence statement. ∆ QRS ≅ ?

Observing the given figure, In ∆ TPQ and ∆ QRS QR = TP (given) ∠ R = ∠ P (given) QS = TQ (given) If two sides and the angle included between the two sides of a triangle are equal to the corresponding two sides and the included angle of another triangle, then the triangles are congruent. So, ∆ QRS ≅ ∆ TPQ by Side-Angle-Side (SAS) congruence condition.

E M B I B E

Mathematics Class 7>Chapter 8 - Congruency of Triangles>Exercise - 4

Telangana Board Solutions for Chapter: Congruency of Triangles, Exercise 9: Exercise - 4

Author:Telangana Board

Telangana Board Mathematics Solutions for Exercise - Telangana Board Solutions for Chapter: Congruency of Triangles, Exercise 9: Exercise - 4

Attempt the practice questions on Chapter 8: Congruency of Triangles, Exercise 9: Exercise - 4 with hints and solutions to strengthen your understanding. Mathematics Class 7 solutions are prepared by Experienced Embibe Experts.

Questions from Telangana Board Solutions for Chapter: Congruency of Triangles, Exercise 9: Exercise - 4 with Hints & Solutions

HARD

7th Telangana Board

IMPORTANT

Mathematics Class 7>Chapter 8 - Congruency of Triangles>Exercise - 4>Q 3

To prove $△ A M P ≅ △ A M Q$ , supply the missing reasons in the following proof.

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Steps	Reasons
(I) $P M = Q M$	(i)
(ii) $∠ P M A ≅ ∠ Q M A$	(ii)
(iii) $A M = A M$	(iii)
(iv) $△ A M P ≅ △ A M Q$	(iv)

MEDIUM

7th Telangana Board

IMPORTANT

Mathematics Class 7>Chapter 8 - Congruency of Triangles>Exercise - 4>Q 5

In the given figure, the two triangles are congruent and the corresponding parts are marked. Find the triangle which is congruent to $△ R A T$ and express it in notation.

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MEDIUM

7th Telangana Board

IMPORTANT

Mathematics Class 7>Chapter 8 - Congruency of Triangles>Exercise - 4>Q 6

In the given figure, the two triangles are congruent and the corresponding parts are marked. Find the triangle which is congruent to $△ A B C$ and express it in notation.

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