Question

for $\triangle pqr$ to be similar to $\triangle tsr$, what must be true?

enter the answer in the space provided. use numbers instead of words.
$pr = square$ inches
$pq = square$ inches
$m\angle prq = square ^\circ$

Explanation:

Step1: Find similarity ratio

$\text{Ratio} = \frac{QR}{SR} = \frac{5}{10} = \frac{1}{2}$

Step2: Calculate length of $PR$

$\frac{PR}{TR} = \frac{1}{2} \implies PR = \frac{1}{2} \times 9 = 4.5$

Step3: Calculate length of $PQ$

$\frac{PQ}{TS} = \frac{1}{2} \implies PQ = \frac{1}{2} \times 6 = 3$

Step4: Find $\angle PRQ$

First, find $\angle SRT$: $180^\circ - 63^\circ - 81^\circ = 36^\circ$.
$\angle PRQ = \angle SRT = 36^\circ$ (vertical angles)

Answer:

$PR = 4.5$ inches
$PQ = 3$ inches
$m\angle PRQ = 36^\circ$