Question

Which similarity statement and justification correctly identifies the triangles'

Answer 1

Answer:

(c) $\triangle ABC$ to $\triangle EDC$ by AA

Step-by-step explanation:

Given

See attachment for triangles

Required

The relationship between both triangles

First, we determine the corresponding sides.

The corresponding sides will be determined based on the length of each side (i.e. bigger sides correspond while smaller sides correspond).

So, we have:

$AC\ to\ EC$

$BC\ to\ DC$

Next, is to name the triangle base on the corresponding sides

The names will be: $\triangle ABC$ and $\triangle EDC$

Lastly, is to check the scale ratio (k).

For both triangles to correspond, the scale ratio must be the same

So:

$k = \frac{EC}{AC} = \frac{DC}{BC}$

$k = \frac{8}{6} = \frac{12}{9}$

$k = \frac{4}{3} = \frac{4}{3}$

$k = \frac{4}{3}$

Hence, the theorem is: $\triangle ABC$ to $\triangle EDC$ by AA