Question

quadrilateral rstq is a parallelogram. which of the following relationships must be true?
$overline{tq}congoverline{qr}$
$overline{rs}congoverline{rq}$
$angle scongangle r$
$angle tcongangle r$

Explanation:

Step1: Recall parallelogram properties

In a parallelogram, opposite - sides are congruent and opposite - angles are congruent.

Step2: Analyze side - length congruence

The pairs of opposite sides in parallelogram \(RSTQ\) are \(\overline{RS}\) and \(\overline{TQ}\), and \(\overline{ST}\) and \(\overline{RQ}\). There is no guarantee that adjacent sides like \(\overline{TQ}\cong\overline{QR}\) or \(\overline{RS}\cong\overline{RQ}\).

Step3: Analyze angle - congruence

The pairs of opposite angles in parallelogram \(RSTQ\) are \(\angle S\) and \(\angle Q\), and \(\angle T\) and \(\angle R\). So, \(\angle T\cong\angle R\).

Answer:

\(\angle T\cong\angle R\)