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 congruent - triangle properties

If \(\triangle PQR\cong\triangle STU\), corresponding sides are equal and corresponding angles are equal.

Step2: Identify corresponding sides and angles

Corresponding sides: \(PQ\) corresponds to \(ST\), \(QR\) corresponds to \(TU\), \(PR\) corresponds to \(SU\). Corresponding angles: \(\angle P\) corresponds to \(\angle S\), \(\angle Q\) corresponds to \(\angle T\), \(\angle R\) corresponds to \(\angle U\).

Step3: Analyze each option

• Option A: Since \(PQ\) and \(ST\) are corresponding sides of congruent triangles \(\triangle PQR\) and \(\triangle STU\), \(PQ = ST\). This is true.
• Option B: \(PQ\) corresponds to \(ST\) and \(TU\) is a different - side. \(PQ

eq TU\). This is false.

• Option C: Since \(\angle R\) and \(\angle U\) are corresponding angles of congruent triangles, \(m\angle R=m\angle U\). This is true.
• Option D: \(\angle P\) corresponds to \(\angle S\), not \(\angle U\). So \(m\angle P

eq m\angle U\). This is false.

• Option E: \(QR\) corresponds to \(TU\), not \(SU\). So \(QR

eq SU\). This is false.

• Option F: Since \(\angle Q\) and \(\angle T\) are corresponding angles of congruent triangles, \(m\angle Q = m\angle T\). So \(m\angle Q

eq m\angle T\). This is false.

Answer:

A. \(PQ = ST\)
C. \(m\angle R=m\angle U\)