Question

question 5 of 10
is △sam ~ △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: Check Angles

In $\triangle SAM$ and $\triangle FIG$, $\angle A = \angle I = 110^\circ$ (given). Now, check the ratios of the sides around the equal angle.
For $\triangle SAM$: sides around $\angle A$ are $SA = 8$, $AM = 12$.
For $\triangle FIG$: sides around $\angle I$ are $FI = 16$, $IG = 24$.

Step2: Calculate Ratios

Calculate $\frac{SA}{FI}=\frac{8}{16}=\frac{1}{2}$ and $\frac{AM}{IG}=\frac{12}{24}=\frac{1}{2}$. Since the included angles are equal and the ratios of the included sides are equal, by SAS (Side - Angle - Side) similarity postulate, the triangles are similar.

Answer:

A. Similar - SAS