Question

1. can you conclude that this parallelogram is a rectangle? explain. yes; the diagonals are perpendicular. no; the diagonals do not bisect two angles of the parallelogram. no; the diagonals may not be congruent. yes; the diagonals are congruent.

Explanation:

Step1: Recall rectangle properties

One property of a rectangle is that its diagonals are congruent. In a parallelogram, if the diagonals are congruent, then it is a rectangle.

Step2: Analyze given options

The first option about perpendicular diagonals is for a rhombus. The second option about diagonals bisecting angles is for a rhombus too. The third option is incorrect as congruent diagonals are a key - factor for a parallelogram to be a rectangle. The fourth option is correct as congruent diagonals in a parallelogram imply it is a rectangle.

Answer:

D. Yes, the diagonals are congruent.