Question

which statement must be true of parallelogram stuv? (1 point)
o $overline{sr}$ must be congruent to $overline{ur}$
o $overline{st}$ must be congruent to $overline{tu}$
o $overline{sr}$ must be congruent to $overline{rt}$
o $overline{vt}$ must be congruent to $overline{su}$

Explanation:

Step 1: Recall parallelogram properties

In a parallelogram, the diagonals bisect each other. Here, the diagonals of parallelogram \(STUV\) are \(SU\) and \(VT\) which intersect at point \(R\). So \(SR = UR\) and \(VR=TR\).

Step 2: Analyze each option

• Option 1: Since the diagonals of a parallelogram bisect each other, \(\overline{SR}\) must be congruent to \(\overline{UR}\). This is a correct property - based on the definition of diagonal - bisection in parallelograms.
• Option 2: In a general parallelogram, adjacent - sides \(\overline{ST}\) and \(\overline{TU}\) are not necessarily congruent. A parallelogram with adjacent - sides congruent is a rhombus.
• Option 3: \(\overline{SR}\) and \(\overline{RT}\) are not related by congruence in a general parallelogram.
• Option 4: In a general parallelogram, the diagonals \(VT\) and \(SU\) are not necessarily congruent. A parallelogram with congruent diagonals is a rectangle.

Answer:

\(\overline{SR}\) must be congruent to \(\overline{UR}\)