In ΔABC, A = 30 , B = 40 and C = 110 In ΔPQR, - Maths - Congruence of Triangles

Question

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?

Gopal Mohanty · Accepted Answer

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

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?

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?