# Diagonals of a parallelogram bisect each other at right angles

Posted on

## Parallelogram

The diagonals of a parallelogram bisect each other

does   online   can

In Euclidean geometry , a parallelogram is a simple non- self-intersecting quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The three-dimensional counterpart of a parallelogram is a parallelepiped. A simple non-self-intersecting quadrilateral is a parallelogram if and only if any one of the following statements is true: [2] [3].

Parallelograms are four-sided shapes that have two pairs of parallel sides. Rectangles, squares and rhombuses are all classified as parallelograms. The classic parallelogram looks like a slanted rectangle, but any four-sided figure that has parallel and congruent pairs of sides can be classified as a parallelogram. Parallelograms have six key properties that distinguish them from other shapes. Opposite sides of all parallelograms -- including rectangles and squares -- must be congruent. Given parallelogram ABCD, if side AB is on the top of the parallelogram and is 9 centimeters, side CD on the bottom of the parallelogram must also be 9 centimeters. This also holds true for the other set of sides; if side AC is 12 centimeters, side BD, which is opposite of AC, must also be 12 centimeters.

## Properties of parallelograms

Diagonals of a parallelogram bisect each other (Theorem and Proof)

In addition, the square is a special case or type of both the rectangle and the rhombus. Here are the properties of the rhombus, rectangle, and square. Note that because these three quadrilaterals are all parallelograms, their properties include the parallelogram properties. All the properties of a parallelogram apply the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary. All the properties of a parallelogram apply the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other. All the properties of a rhombus apply the ones that matter here are parallel sides, diagonals are perpendicular bisectors of each other, and diagonals bisect the angles.

The angles of quadrilateral are in the ratio 3 : 5 : 9 : quadrilateral. If the diagonals of a parallelogram are equal, then show that it is a rectangle. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus. Show that the diagonals of a square are equal and bisect each other at right angles. Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. Thus, ABCD is a square.

## Ex 8.1, 4 - Chapter 8 Class 9 Quadrilaterals

One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel. If we have a parallelogram where all sides are congruent then we have what is called a rhombus. 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.

Class 9 - Maths - Quadrilaterals. Download PDF. The angles of quadrilateral are in the ratio 3: 5: 9: Find all the angles of the quadrilateral. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Geometry and measurement : Module 21 Years : PDF Version of module. The material in this module is a continuation of the module, Parallelograms and Rectangles , which is assumed knowledge for the present module. Thus the present module assumes:. Logical argument, precise definitions and clear proofs are essential if one is to understand mathematics. These analytic skills can be transferred to many areas in commerce, engineering, science and medicine but most of us first meet them in high school mathematics.

.

## 1 thoughts on “Diagonals of a parallelogram bisect each other at right angles”

1. No, as a general rule the diagonals of a parallelogram do not bisect each other at right angles. The definition of a parallelogram is a four-sided.