Question

12 multiple choice 1 point find the length of $overline{qr}$ in the figure. figure description with line - segment lengths: $ps = 15$, $pq = 7$, $rs = 12$ 12 units 8 units 4 units 5 units 13 multiple choice 1 point given that $\triangle def$ is congruent to $\triangle pqr$, find the angle that is congruent to $angle e$. figure of two triangles $\triangle def$ and $\triangle pqr$ $angle p$ $angle r$ $angle q$ $angle f$

Explanation:

Step1: Identify relevant lengths

We know that $PS = 15$, $PQ=7$ and $PR = 12$.

Step2: Use segment - addition postulate

Since $PR=PQ + QR$, then $QR=PR - PQ$.
Substitute $PR = 12$ and $PQ = 7$ into the formula: $QR=12 - 7$.
$QR = 5$.

For the second question:
When $\triangle DEF\cong\triangle PQR$, corresponding angles are congruent. The order of the vertices in the congruence statement $\triangle DEF\cong\triangle PQR$ gives the correspondence. $\angle D$ corresponds to $\angle P$, $\angle E$ corresponds to $\angle Q$, and $\angle F$ corresponds to $\angle R$.

Answer:

1. D. 5 units
2. C. $\angle Q$