# Do parallelograms have perpendicular diagonals?

## Do parallelograms have perpendicular diagonals?

The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.

## What is it called when a parallelogram has perpendicular diagonals?

‘If the diagonals of a parallelogram are perpendicular, then it is a rhombus. ‘

How do you prove that the diagonals of a parallelogram are perpendicular?

= A · A – B · B. Therefore, (A + B) · (A – B)=0 ⇔ A · A = B · B. I.e., the diagonals are perpendicular if and only if two adjacent edges have equal lengths. In other words, if the parallelogram is a rhombus.

What are three properties of a parallelogram?

The parallelogram has the following properties:

• Opposite sides are parallel by definition.
• Opposite sides are congruent.
• Opposite angles are congruent.
• Consecutive angles are supplementary.
• The diagonals bisect each other.

### What are the properties of a parallelogram on a rhombi?

The properties of parallelograms can be applied on rhombi. If we have a quadrilateral where one pair and only one pair of sides are parallel then we have what is called a trapezoid. The parallel sides are called bases while the nonparallel sides are called legs.

### Which is the most important property of a parallelogram?

There are six important properties of parallelograms to know: Opposite sides are congruent (AB = DC). Opposite angels are congruent (D = B). Consecutive angles are supplementary (A + D = 180°).

How to prove the opposite sides are equal in a parallelogram?

To Prove: The opposite sides are equal, AB=CD, and BC=AD. Proof: In parallelogram ABCB, compare triangles ABC and CDA. In these triangles AC = CA (common sides). Also ∠BAC =∠DCA (alternate interior angles), and ∠BCA = ∠DAC (alternate interior angles).

Are there any theorems about a parallelogram?

Theorem 1: In a Parallelogram the Opposite Sides Are Equal. This means, in a parallelogram, the opposite sides are equal. Given: ABCD is a parallelogram.

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