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

Step-by-step explanation:

Refer the attached figure :

In Δ ABD ,

∠B=∠D = 66°

By property : opposite sides of equal angles are equal

Thus AB=AC

In Δ CBD ,

∠B=∠D = 66°

By property : opposite sides of equal angles are equal

Thus CB=CD  

Thus all four sides of quadrilateral ABCD are equal

And diagonal BD bisects the angles

So, it is a rhombus

Thus Option c is correct .

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

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.