A. Explain how you know that Triangle ABC is similar to Triangle A'B'C'. (use complete sentences and show all your work to get full credit) B. If AC = 8, A'C' = 12, and AB = 20 what is the length of A'B'?

A. Since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.

B. A'B' = 30

Step-by-step explanation:

A. Two triangles are said to be similar if their corresponding angles are congruent to each other.

To know whether ∆ABC and ∆A'B'C' are similar, let's find the measure of their angles each, and see if their corresponding angles are congruent to each other.

∆ABC:

m<A = 59°

m<B = 37°

m<C = 180 - (37 + 59) = 84°

∆A'B'C':

m<A' = 59°

m<B' = 180 - (59 + 84) = 37°

m<C' = 84°

As we can see,

Angle A is congruent to Angle A'

Angle B is congruent to Angle B'

Angle C is congruent to Angle C'

Therefore, since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.

B. AC = 8; A'C' = 12; AB = 20

Since ∆ABC is similar to ∆A'B'C', the ratio of their corresponding sides would be equal.

Therefore:

AC/A'C' = AB/A'B'

Plug in the values into the equation

8/12 = 20/A'B'

Cross multiply

A'B'*8 = 20*12

A'B'*8= 240

Divide both sides by 8

A'B' = 240/8

A'B' = 30