Question

How can the angle-angle similarity postulate be used to prove the two triangles are similar? Explain your answer using complete sentences, and provide evidence to support your claims.

Answer 1

AA (Angle-Angle) Similarity. In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar . (Note that if two pairs of corresponding angles are congruent, then it can be shown that all three pairs of corresponding angles are congruent, by the Angle Sum Theorem.)

Answer 2

Explanation:

Given :

In triangle ABC, ∠A = 32°,

∠B = 49°

In triangle A'B'C',

∠B' = 49°

∠C' = 99°

To prove : ΔABC and ΔA'B'C' are similar.

Proof :

In triangle ABC,

∠A = 32° and ∠B = 49°

Then ∠C = 180° - (∠A + ∠B)

= 180° - (32° + 49°)

= 180° - 81°

= 99°

Similarly, in ΔA'B'C'

∠B' = 49° and ∠C' = 99°

Then ∠A' = 180° - (99° + 49°)

= 180° - 148°

= 32°

Now we find ∠A ≅ ∠A' ≅ 32°

∠B ≅ ∠B' ≅ 49°

and ∠C ≅ ∠C' ≅ 99°

Therefor, by both the triangles ABC and A'B'C' will be similar.