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