Question

Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.

Answer 1

The correct option is parallelogram ABCD is a rhombus, because the diagonal bisects two angles

Explanation:

In triangle ABD:

∠B = ∠D

Thus AB=AC by the property of opposite sides of equal angles are equal

In triangle CBD

∠B = ∠D

Thus CB=CD by the property of opposite sides of equal angles are equal

Thus all four sides of quadrilateral ABCD are equal

And diagonal BD bisects the angles

So, it is a rhombus

Therefore the correct option is parallelogram ABCD is a rhombus, because the diagonal bisects two angles....