Question

the triangles are similar by...
a) sss
c) sas
b) asa
d) aa
13.
side - angle - side (sas)
if two sides of one triangle are proportional to two corresponding sides of another triangle, and their corresponding included angles are congruent, the two triangles are similar
14.
if the triangles are similar, state how.
a) not similar.
c) sss
b) sas
d) aa

Explanation:

Step1: Check side - side - side (SSS) similarity

For SSS similarity, we need to check if the ratios of corresponding sides are equal. For the two triangles in question 14, the ratios of corresponding sides are $\frac{12}{36}=\frac{1}{3}$ and $\frac{15}{45}=\frac{1}{3}$.

Step2: Analyze the similarity criterion

Since the ratios of all three pairs of corresponding sides of the two triangles are equal, the triangles are similar by SSS (Side - Side - Side) similarity criterion.

Answer:

1. No information about side - lengths or angles of the triangles in question 13 is given in the description, so we cannot answer it.
2. c) SSS