Question

The parallelogram has the angle measures shown. Can you conclude that it is a rhombus, a

Answer 1

The given parallelogram is a rhombus

Solution:

Option A: Rhombus

Let us recall the property of rhombus.

• Diagonals bisect each other at right angles.
• Opposite angles are congruent.

Here diagonals bisect the angles equally each 72°.

Opposite angles are congruent(72° + 72° = 144°).

Hence the given parallelogram is a rhombus.

Option B: Rectangle

Let us recall the property of rectangle.

• Diagonals bisect each other.
• All the angles of a rectangle are 90°.

Here 72° + 72° = 144°, not 90°.

So, the given parallelogram is not a rectangle.

Option C: Square

Let us recall the property of square.

• Diagonals bisect each other.
• All the angles of a square are 90°.

Here 72° + 72° = 144°, not 90°.

So, the given parallelogram is not a square.