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

Explanation with Proof is given below.

Step-by-step explanation:

Given:

In  Δ ABC,

m∠ A = 59°

m∠ B = 37°

In Δ A'B'C'

m∠ A' = 59°

m∠ C' = 84°

To Prove:

Δ ABC ~ Δ A'B'C'

Proof:

In  Δ ABC we have,

m∠ A + m∠ B + m∠ C = 180° {Angle Sum Property of Triangle}

Substituting the given values we get

Now,

In  Δ ABC and Δ  A'B'C'

∠ A ≅ ∠ A'     …………..{measure of each angle is 59°}

∠ C ≅ ∠ C'     ……….{measure of each angle is 84°}

Δ ABC ~ Δ A'B'C'  ….{ By Angle-Angle Similarity Postulate} Proved

12/11c

or

12

c

11