Question

state if the triangles in each pair are similar. if so, state how you know they are similar and complete the similarity statement.
1)

△pqr ~ ______

Explanation:

Step1: Check Vertical Angles

$\angle FPE$ and $\angle QPR$ are vertical angles, so $\angle FPE = \angle QPR$.

Step2: Check Proportional Sides

Calculate the ratios of corresponding sides:

• $\frac{FP}{QP} = \frac{5}{20} = \frac{1}{4}$
• $\frac{EP}{RP} = \frac{8}{32} = \frac{1}{4}$

Since two sides are in proportion and the included angle is equal (SAS Similarity Criterion), the triangles are similar.

Step3: Determine Similar Triangle

By SAS similarity, $\triangle PQR \sim \triangle PFE$.

Answer:

$\triangle PFE$ (The triangles are similar by SAS similarity because $\angle FPE = \angle QPR$ and $\frac{FP}{QP} = \frac{EP}{RP} = \frac{1}{4}$)