In ABC, ∠ A = 30 o , ∠ B = 40 o and ∠ C = 110 o . In , ∠ P = 30 o , ∠ Q = 40 o and ∠ R = 110 o . A student says that by AAA congruence criterion. Is he justified? Why or why not?

Question

In ABC, &#x2220; A = 30 o , &#x2220; B = 40 o and &#x2220; C = 110 o . In , &#x2220; P = 30 o , &#x2220; Q = 40 o and &#x2220; R = 110 o . A student says that by AAA congruence criterion. Is he justified? Why or why not?

Philoid · Accepted Answer

According to the question, in ABC, ∠A = 30^o, ∠B = 40^o and ∠C = 110^o

And, in , ∠P = 30^o, ∠Q = 40^o and ∠R = 110^o

We have to justify that:

Is , by AAA congruence rule

As the given property shows that the two triangles have their all three respective angles equal.

But, no information explains about any of the sides.

Thus, it can be concluded that, AAA Property do not proves the triangle to be congruent.

In ABC, ∠A = 30o, ∠B = 40o and ∠C = 110o. In, ∠P = 30o, ∠Q = 40o and ∠R = 110o. A student says that by AAA congruence criterion. Is he justified? Why or why not?

In ABC, ∠A = 30^o, ∠B = 40^o and ∠C = 110^o. In, ∠P = 30^o, ∠Q = 40^o and ∠R = 110^o. A student says that by AAA congruence criterion. Is he justified? Why or why not?