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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.

How can the angleangle similarity postulate be used to prove the two triangles are similar Explain your answer using complete sentences and provide evidence to class=

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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:

Step-by-step 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.

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