Question

question 4 of 10
is $\triangle pqr \sim \triangle xyz$? if so, name which similarity postulate or theorem applies.
a. similar - aa
b. similar - sss
c. similar - sas
d. cannot be determined

Explanation:

Step1: Identify corresponding sides

For $\triangle PQR$ and $\triangle XYZ$, the sides adjacent to the 80° angle are:
$PQ=3$, $PR=5$ for $\triangle PQR$; $XY=6$, $XZ=10$ for $\triangle XYZ$.
Calculate the ratios:
$\frac{PQ}{XY} = \frac{3}{6} = \frac{1}{2}$
$\frac{PR}{XZ} = \frac{5}{10} = \frac{1}{2}$

Step2: Identify included angles

The included angle between the sides is $\angle P = 80^\circ$ and $\angle Y = 80^\circ$, so $\angle P = \angle Y$.

Step3: Match to similarity postulate

Two pairs of corresponding sides are proportional, and the included angles are congruent, which fits the SAS Similarity Postulate.

Answer:

C. Similar - SAS