Question

quadrilateral rstq is a parallelogram. which of the following relationships must be true? ∠r≅∠q rs≅st tq≅ts ∠s≅∠q

Explanation:

Step1: Recall parallelogram properties

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

Step2: Analyze angle - side relationships

For parallelogram \(RSTQ\), \(\angle R\) and \(\angle Q\) are opposite angles, \(\overline{RS}\) and \(\overline{TQ}\) are opposite sides, \(\overline{ST}\) and \(\overline{RQ}\) are opposite sides.

• Opposite angles of a parallelogram are congruent. So \(\angle R\cong\angle Q\) and \(\angle S\cong\angle T\).
• Opposite sides of a parallelogram are congruent. So \(\overline{RS}\cong\overline{TQ}\) and \(\overline{ST}\cong\overline{RQ}\).
• The statements \(\overline{RS}\cong\overline{ST}\), \(\overline{TQ}\cong\overline{TS}\) are not always true as adjacent sides of a parallelogram are not necessarily congruent. And \(\angle S\cong\angle Q\) is not true as they are not opposite angles.

Answer:

\(\angle R\cong\angle Q\)