Question

parallelogram abcd has the angle measures shown. can you conclude that it is a rhombus, a rectangle, or a square? explain. there is not enough information. parallelogram abcd is a rectangle because the diagonal creates congruent angles. parallelogram abcd is a square because all four angles have the same measure. parallelogram abcd is rhombus because the diagonal bisects two angles.

Explanation:

Step1: Recall properties of shapes

A rectangle has four right - angles (90° each). A square has four right - angles and all sides equal. A rhombus has all sides equal and its diagonals bisect the angles.

Step2: Analyze given angle measures

The given angles are 59°, not 90°. So it is not a rectangle or a square.

Step3: Apply rhombus property

Since the diagonal of the parallelogram creates congruent angles (59° each), it means the diagonal bisects the angles of the parallelogram. This is a property of a rhombus.

Answer:

D. Parallelogram ABCD is a rhombus because the diagonal bisects two angles.