Question

triangle pqr is reflected across the line ( y = 0 ). the image is then translated 5 units to the right, resulting in ( \triangle stu ). which of the following statements are true? select all that apply.
a ( pq = st )
b ( pq = tu )
c ( mangle r=mangle u )
d ( mangle p=mangle u )

Explanation:

Step1: Understand transformation properties

Reflections and translations are rigid transformations. Rigid transformations preserve side - lengths and angle - measures. So, \(\triangle PQR\cong\triangle STU\).

Step2: Analyze side - length congruence

If \(\triangle PQR\cong\triangle STU\), then corresponding sides are equal. \(PQ\) corresponds to \(ST\) (by the order of the congruence \(\triangle PQR\cong\triangle STU\), \(P\) corresponds to \(S\), \(Q\) corresponds to \(T\)). So \(PQ = ST\). \(PQ\) does not correspond to \(TU\).

Step3: Analyze angle - measure congruence

If \(\triangle PQR\cong\triangle STU\), then corresponding angles are equal. \(\angle R\) corresponds to \(\angle U\) (by the order of the congruence \(\triangle PQR\cong\triangle STU\), \(R\) corresponds to \(U\)). So \(m\angle R=m\angle U\). \(\angle P\) corresponds to \(\angle S\), not \(\angle U\).

Answer:

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