Question

1. can you conclude that this parallelogram is a rectangle? explain.

yes; the diagonals are perpendicular.
yes; there are four right angles given.
no; the diagonals may not be congruent.
yes; the diagonals bisect two angles of the parallelogram.

Explanation:

Step1: Recall rectangle properties

A parallelogram is a rectangle if and only if its diagonals are congruent. There is no information given about the diagonals being congruent in the problem. The fact that diagonals are perpendicular makes a parallelogram a rhombus, diagonals bisecting angles also relates to rhombus - like properties, and no right - angles are indicated.

Answer:

No; the diagonals may not be congruent.