A rhombus is a special kind of parallelogram, in which all the sides are equal. We've seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. Here we will … [Read more...] about A Parallelogram with Perpendicular Diagonals is a Rhombus

# Rhombus

A parallelogram in which all the edges are of equal length is called a rhombus, or a diamond.

In addition to the general properties of parallelograms, in a rhombus, the diagonals bisect the angles, and the diagonals are perpendicular to each other.

We will show these properties using triangle congruence.

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*Now that we've explained the basic concept of rhombus in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## Properties of Rhombus: The Opposite Angles are Congruent

We have shown that in any parallelogram, the opposite angles are congruent. Since a rhombus is a special kind of parallelogram, it follows that one of its properties is that both pairs of opposite … [Read more...] about Properties of Rhombus: The Opposite Angles are Congruent

## Diagonals of a Rhombus are Perpendicular to Each Other

We have shown that in a rhombus the diagonals bisect the angles, using triangle congruency. We can follow the same procedure to prove that the diagonals of a rhombus are perpendicular to each … [Read more...] about Diagonals of a Rhombus are Perpendicular to Each Other

## Rhombus Diagonals Bisect the Angles

A Rhombus has two axes of symmetry, created by the diagonals. Since it is symmetrical, the diagonals bisect the angles, as we will show using triangle congruence. Problem In a rhombus ABCD, … [Read more...] about Rhombus Diagonals Bisect the Angles