Question

use the graph of two triangles for items 1 and 2. select all the true statements given that △pqr≅ △stu. a pq = st b pq = tu c m∠r = m∠u d m∠p = m∠u e qr = su f m∠q = m∠t

Explanation:

Step1: Recall property of congruent triangles

If $\triangle PQR\cong\triangle STU$, then corresponding - sides are equal and corresponding - angles are equal. That is, $PQ = ST$, $QR=TU$, $PR = SU$, $\angle P=\angle S$, $\angle Q=\angle T$, $\angle R=\angle U$.

Step2: Check each option

• Option A: Since $\triangle PQR\cong\triangle STU$, $PQ$ and $ST$ are corresponding sides, so $PQ = ST$. This option is True.
• Option B: $PQ$ and $TU$ are not corresponding sides. So $PQ

eq TU$. This option is False.

• Option C: $\angle R$ and $\angle U$ are corresponding angles. So $m\angle R=m\angle U$. This option is True.
• Option D: $\angle P$ and $\angle U$ are not corresponding angles. So $m\angle P

eq m\angle U$. This option is False.

• Option E: $QR$ and $SU$ are not corresponding sides. So $QR

eq SU$. This option is False.

• Option F: $\angle Q$ and $\angle T$ are corresponding angles. So $m\angle Q=m\angle T$. This option is True.

Answer:

A. $PQ = ST$
C. $m\angle R=m\angle U$
F. $m\angle Q=m\angle T$