Why rhombus is a parallelogram

What kind of quadrilateral is made? Figure From the picture, it looks kind of like a parallelogram. You have to be careful, though, because looks can be deceiving. It also looks like the diagonals of the newly created quadrilateral are perpendicular. If the drawing is accurate, you might be tempted to conclude that the quadrilateral is a rhombus. Let's prove it. You need a serious game plan for this one. Because you're dealing with a rectangle, you know that m?

So by the SAS Postulate,? So opposite sides are congruent and quadrilateral MNOP is a parallelogram. Also, adjacent sides are congruent, so parallelogram MNOP is a rhombus. All rights reserved including the right of reproduction in whole or in part in any form. Parallelogram Rhombus In a parallelogram , opposite sides are equal in measure. In a rhombus , all sides are equal in measure Diagonals bisect each other. Diagonals bisect each other at 90 degrees.

The perimeter of a rhombus is equal to 4x where x is the measure of each side of a rhombus. Every parallelogram is not a rhombus. Every rhombus is a parallelogram. Both rhombus and parallelogram are four-sided quadrilaterals with opposite sides parallel, opposite angles equal, the sum of their interior angles is 0. But taking into account some of the properties of rhombus and parallelogram we can justify that rhombus and a parallelogram are two different types of quadrilateral. Rhombus and parallelograms are closely related to each other but they are still different.

The main difference between them is rhombus is a quadrilateral with all its four sides equal while parallelogram has its opposite sides equal. Now let us explain the difference between a parallelogram and a rhombus. Rhombus and parallelograms are two different quadrilaterals. Some of the key difference between rhombus and parallelogram are:. Rhombus is a flat two-dimensional figure, where all its four sides are parallel to each other.

A parallelogram is a flat- two-dimensional figure, whose only opposite sides are parallel to each other. All the four sides are of equal lengths. Opposite sides are of equal lengths. Diagonals bisect each other at the right angle, forming two scalene triangles. Diagonals bisect each other, forming congruent triangles.

Every rhombus will be a parallelogram. Every parallelogram will not be a rhombus. Solved Examples. Identify the Below Figure is a Rhombus or a Parallelogram.

Solution : In Quadrilateral above. All of its sides are equal.