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In Triangle Abc, ∠A = 30°, ∠B = 40° and ∠C = 110° in Triangle Pqr, ∠P = 30°, ∠Q = 40° and ∠R = 110° a Student Says that Triangle Abc ≅ Triangle Pqr by Aaa Congruence Criterion. is He Justified? Why Or Why Not? - Mathematics

In ΔABC, ∠A = 30°, ∠B = 40° and ∠C = 110°

In ΔPQR, ∠P = 30°, ∠Q = 40° and ∠R = 110°

A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?

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Solution

No. This property represents that these triangles have their respective angles of equal measure. However, this gives no information about their sides. The sides of these triangles have a ratio somewhat different than 1:1. Therefore, AAA property does not prove the two triangles congruent.

Concept: Criteria for Congruence of Triangles
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APPEARS IN

NCERT Class 7 Maths
Chapter 7 Congruence of Triangles
Exercise 7.2 | Q 4 | Page 150
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