The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.
A parallelogram is drawn with a horizontal diagonal from the left to right vertices. Each of the four angles formed by a side and the diagonal at the left or right vertex is 72 degrees.
We cannot conclude that the parallelogram is a rhombus, rectangle, or square with only this information. However, we do know that opposite angles of a parallelogram are congruent, so the opposite angles to the 72 degree angles must also measure 72 degrees. Additionally, the sum of the angles in a parallelogram is always 360 degrees. Thus, we know that the other two angles in the parallelogram measure 144 degrees each.
If we had additional information, we could potentially determine if the parallelogram is a rhombus, rectangle, or square. For example, if we knew that all sides of the parallelogram were congruent (i.e. a rhombus), or that the diagonals were perpendicular (i.e. a rectangle or square), we could draw conclusions about its shape.