A rectangle has two diagonals. Each one is a line segment drawn between the opposite vertices (corners) of the rectangle. **Each diagonal divides the rectangle into two congruent right triangles**. Because the triangles are congruent, they have the same area, and each triangle has half the area of the rectangle.

Contents

- 1 What do diagonals equal in a rectangle?
- 2 Do the diagonals of a rectangle bisect the angle?
- 3 Do the diagonals of a rectangle meet?
- 4 Are diagonals of a rectangle congruent?
- 5 Why are the diagonals of a rectangle equal?
- 6 What are properties of a rectangle?
- 7 Do rectangles have perpendicular diagonals?
- 8 What is the relationship between the rectangle and its sides?
- 9 How do you work out diagonals?
- 10 How do you find the diagonal of a rectangle?
- 11 What are necessary when proving that the diagonals of a rectangle are congruent?
- 12 What does it mean if diagonals are congruent?

## What do diagonals equal in a rectangle?

A rectangle is a parallelogram, so its opposite sides are equal. The diagonals of a rectangle are equal and bisect each other.

## Do the diagonals of a rectangle bisect the angle?

The diagonals of a rectangle are congruent. Some properties of rectangles are mentioned in the points below. Each of the interior angles of a rectangle is 90° making the sum of interior angle to be 360°. The diagonals of a rectangle bisect each other.

## Do the diagonals of a rectangle meet?

As you can see from the pictures to the left, the diagonals of a rectangle do not intersect in a right angle (they are not perpendicular). (Unless the rectangle is a square.) And the angles formed by the intersection are not always the same measure (size). Opposite central angles are the same size (they are congruent.)

## Are diagonals of a rectangle congruent?

The rectangle has the following properties: All angles are right angles by definition. The diagonals are congruent.

## Why are the diagonals of a rectangle equal?

Yes, the diagonals of a rectangle are equal. This is because the two diagonals are the hypotenuse of the two right angled triangles formed by the diagonals. Hence, the diagonals of the rectangle are equal in length.

## What are properties of a rectangle?

A square is a special case of an isosceles trapezoid, kite, parallelogram, quadrilateral, rectangle, rhombus, and trapezoid. The diagonals of a square bisect one another and are perpendicular (illustrated in red in the figure above). In addition, they bisect each pair of opposite angles (illustrated in blue).

## Do rectangles have perpendicular diagonals?

The diagonals of a rectangle are perpendicular to each other.

## What is the relationship between the rectangle and its sides?

All the four angles of the rectangle are right angles or equal to 90 degrees. The opposite sides of the rectangle are equal and parallel to each other.

## How do you work out diagonals?

You can use the Pythagorean theorem to estimate the diagonal of a rectangle, which can be expressed with the following formula: d² = l² + w², and now you should know how to find the diagonal of a rectangle explicit formula – just take a square root: d = √(l² + w²).

## How do you find the diagonal of a rectangle?

You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

## What are necessary when proving that the diagonals of a rectangle are congruent?

The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB. Since ABCD is a rectangle, it is also a parallelogram. Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

## What does it mean if diagonals are congruent?

Properties of a Rectangle The diagonals are congruent and bisect each other (divide each other equally). Opposite angles formed at the point where diagonals meet are congruent. A rectangle is a special type of parallelogram whose angles are right.