Question

question 7 of 10
is ( \triangle samsim\triangle fig )? if so, identify the similarity postulate or theorem that applies.

a. similar - sas
b. similar - sss
c. similar - aa
d. cannot be determined

Explanation:

Step1: Calculate the ratio of corresponding sides

In \(\triangle SAM\) and \(\triangle FIG\), we have \(\frac{SA}{FI}=\frac{8}{16}=\frac{1}{2}\) and \(\frac{AM}{IG}=\frac{12}{24}=\frac{1}{2}\).

Step2: Check the included angle

The included angle \(\angle A = 110^{\circ}\) and \(\angle I=110^{\circ}\), so \(\angle A=\angle I\).

Since the ratio of two pairs of corresponding sides is equal (\(\frac{SA}{FI}=\frac{AM}{IG}=\frac{1}{2}\)) and the included angles are equal (\(\angle A=\angle I\)), by the SAS (Side - Angle - Side) similarity postulate, \(\triangle SAM\sim\triangle FIG\).

Answer:

A. Similar - SAS