Question

Name the postulate or theorem that proves each pair of triangles similar. Explain your reasoning.

Answer 1

The postulate or theorem that proves each pair of triangles similar is Side-Angle-Side similarity theorem.

$\begin{gathered} \text{Tan }\angle M=\frac{15}{21}=\frac{5}{7} \\ \text{Tan }\angle L=\frac{15+5}{28}=\frac{20}{28}=\frac{5}{7} \end{gathered}$

Since angle M and angle L are acute, then

$\angle M\cong\angle L$