Question

not similar or not necessarily similar
○ not similar
○ similar:
△abc ~ △ by the
select

part 2 of 2
not similar or not necessarily similar
○ not similar
○ similar:
△prq ~ △ by the

Explanation:

Step1: Compare side ratios (Left Pair)

Calculate ratios of corresponding sides:
$\frac{AB}{DE} = \frac{5}{10} = \frac{1}{2}$, $\frac{AC}{DF} = \frac{7}{7} = 1$, $\frac{BC}{EF} = \frac{6}{8} = \frac{3}{4}$

Step2: Check similarity (Left Pair)

Since $\frac{1}{2}
eq 1
eq \frac{3}{4}$, sides are not proportional.

Step3: Compare side ratios (Right Pair)

Calculate ratios of corresponding sides:
$\frac{PR}{TU} = \frac{9}{18} = \frac{1}{2}$, $\frac{PQ}{UT} = \frac{5}{10} = \frac{1}{2}$, $\frac{RQ}{TU} = \frac{7}{14} = \frac{1}{2}$

Step4: Check similarity (Right Pair)

All side ratios are equal ($\frac{1}{2}$), so sides are proportional.

Answer:

Part 1:

Not similar or not necessarily similar

Part 2:

Similar: $\triangle PRQ \sim \triangle TSU$ by the Side-Side-Side (SSS) Similarity Criterion