Question

what are the corresponding parts of the figures below? select all that apply.
r
59°
32 cm
23 cm
y
32 cm
44°
59°
23 cm
28 cm
77°
44°
28 cm
p
q
77°
w
x
pq≅yw
pq≅wx
rp≅wx
∠q≅∠y

Explanation:

Step1: Match side - lengths

In $\triangle PQR$, $PQ = 28$ cm, $RP=23$ cm, $RQ = 32$ cm. In $\triangle WXY$, $YW = 23$ cm, $WX = 32$ cm, $YX=28$ cm. So, $\overline{PQ}\cong\overline{YX}$, $\overline{RP}\cong\overline{YW}$, $\overline{RQ}\cong\overline{WX}$.

Step2: Match angles

In $\triangle PQR$, $\angle P = 77^{\circ}$, $\angle Q=44^{\circ}$, $\angle R = 59^{\circ}$. In $\triangle WXY$, $\angle W = 77^{\circ}$, $\angle X=44^{\circ}$, $\angle Y = 59^{\circ}$. So, $\angle P\cong\angle W$, $\angle Q\cong\angle X$, $\angle R\cong\angle Y$.

Answer:

$\overline{PQ}\cong\overline{YX}$, $\overline{RP}\cong\overline{YW}$, $\overline{RQ}\cong\overline{WX}$, $\angle P\cong\angle W$, $\angle Q\cong\angle X$, $\angle R\cong\angle Y$