Do Rectangle Diagonals Bisect Angles

Diagonal of Rectangle

The diagonal of rectangle is a line segment that connects the two contrary vertices of the rectangle. The diagonal of the rectangle divides the rectangle into two equal right triangles. A rectangle is a two-dimensional figure with four sides, four vertices, and four angles. The two diagonals of a rectangle have the same length.

In this commodity, we will understand the concept of diagonal of a rectangle and the method to calculate its length. We shall explore the properties, formula, and derivation of the formula to evaluate the length of the diagonal of a rectangle. Allow u.s. larn more than about the diagonals of a rectangle, their formula, and solve a few examples.

ane.	What are Diagonals of Rectangle?
two.	Diagonals of Rectangle Properties
3.	Diagonal of Rectangle Formula
iv.	Diagonal of Rectangle Derivation
5.	Angles of Diagonals of Rectangle
6.	FAQs on Diagonals of Rectangle

What is Diagonal of Rectangle?

The diagonal of a rectangle is a line segment that joins any two of its non-next vertices. A rectangle has two diagonals where each of the diagonals divides the rectangle into two right-angled triangles with the diagonal being the hypotenuse. The diagonals bifurcate each other, making i birdbrained bending and the other an acute angle. The ii triangles formed past the diagonal of rectangle are congruent.

Diagonal of Rectangle

Diagonals of Rectangle Properties

The diagonal of rectangle is a line segment drawn between the opposite vertices of the rectangle. The properties of diagonals of a rectangle are every bit follows:

The two diagonals of a rectangle are coinciding. In other words, the length of the diagonals is equal.
The ii diagonals bisect each other and divide the rectangle into ii equal parts.
The length of the diagonal of rectangle can be obtained using the Pythagoras theorem.
When the diagonals bisect each other, the angles of a rectangle at the heart become one obtuse angle and the other an acute angle.
When two diagonals bisect each other at 90° it is called a square.
Since the diagonal of rectangle split the rectangle into 2 right-angled triangles, it is considered the hypotenuse of these triangles.

Diagonal of Rectangle Formula

The diagonal of a rectangle formula helps in finding the length and width of the rectangle. In the following rectangle, Air-conditioning and BD are the diagonals. You tin meet that the lengths of both AC and BD are the same. A diagonal cuts a rectangle into ii right triangles, in which the sides are equal to the sides of the rectangle and with a hypotenuse. That hypotenuse is the diagonal.

Diagonal of Rectangle Formula

Thus, to calculate the length of diagonals of a rectangle the formula is: d = √( l² + w²)

Where,

d = diagonal of rectangle
l = length of the rectangle
westward = width of the rectangle

Diagonal of Rectangle Derivation

The diagonal of a rectangle formula is derived using the Pythagoras theorem. Consider the rectangle given higher up. Let u.s.a. consider a rectangle of length "50" and width "due west". Let the length of each diagonal be "d".

Applying Pythagoras theorem to the triangle BCD,

d² = l² + westward²

Taking square root on both sides,

d = √( 50² + w²)

Thus, the diagonal of a rectangle formula is:

d = √( lⁱⁱ + w²)

Where,

l = length of the rectangle
west = width of the rectangle

Angles of Diagonal of Rectangle

The diagonals of a rectangle are of equal length and they bisect each other simply do not form right angles at the center. They form linear pairs of angles such as obtuse bending + astute bending at each of the diagonal. The rectangle is chosen a square if its diagonals bisect each other at correct angles equally the diagonals of a rectangle practise not bisect the respective vertex angles into equal angles.

A diagonal divides a rectangle into two coinciding triangles, that too right triangles with their hypotenuse being the same. Each diagonal acts as the hypotenuse for the correct triangles so formed. Applying Pythagoras theorem to the triangle so formed, d² = l² + w², where d is diagonal, l is length and due west is the width of the rectangle. Taking square root on both sides, √(d²) = √( l^two + westⁱⁱ). Thus, the diagonal of a rectangle formula is: √( l² + due west²).

Important Notes on Diagonal of Rectangle

The diagonal of rectangle is a line segment joining the non-adjacent vertices.
Nosotros tin can calculate the length of the diagonal of rectangle using the formula, d = √( 50² + w²).
The two diagonals of rectangle bisect each other.

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Angles of Rectangle
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Diagonals of Rectangle Examples

Example i: Using the diagonal of rectangle formula, find the diagonal of a rectangle whose dimensions are 3 units and 4 units.

Solution:

The dimensions of a rectangle = 3 units and 4 units.
Co-ordinate to the properties of angles of the rectangle, the diagonal of a rectangle = (d) = √( l² + w²)
Length of diagonal of rectangle = √(iii)²+(four)ⁱⁱ = √25 = 5 units.

Answer: Therefore, the length of the diagonal of the rectangle is 5 units.
Instance 2: The size of the screen of a goggle box is the length of its diagonal. So discover the size of the television whose dimensions are 18 inches and 46 inches.

Solution:

The length of the television, l = 46 units.

The width of the telly, w = 18 units.

Using the diagonal of a rectangle formula,

d = √( fiftyⁱⁱ + west²)

d = √( 46² + xviiiⁱⁱ)

= √2440

= 49.39 inches.

Answer: Therefore, the size of the television is 49.39 inches.
Example 3: If a rectangular board has a length of 13 inches with a diagonal of xviii inches. What is the width of the rectangle?

Solution:

The length of the board, 50 = thirteen inches.

The diagonal of the board, d = xviii inches.

Using the diagonal of rectangle formula,

d = √( fifty² + w^two)

18² = (13² + due west^two)

w = √155

w = 12.4 inches.

Reply: Therefore, the width of the rectangle is 12.4 inches.

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Exercise Questions on Diagonals of Rectangle

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FAQs on Diagonals of Rectangle

What is the Diagonal of Rectangle?

The diagonal of a rectangle is a line segment that is fatigued from the opposite vertices of the rectangle and bisect the other diagonal. There are two diagonals of a rectangle that are of the same length and separate the rectangle into two equal parts. The diagonal of the rectangle divides the rectangle into two right-angled triangles with a hypotenuse.

What is the Diagonal Formula of Rectangle?

The formula to calculate the diagonal of rectangle helps in finding the length of the diagonal. The formula is:

d = √( l² + westward^two)

Where,

d = diagonal of rectangle
l = length of the rectangle
due west = width of the rectangle

What are the Properties of Diagonal of Rectangle?

The backdrop of the diagonal of rectangle are:

The length of the two diagonals is equal.
The two diagonals bisect each other and divide the rectangle into 2 equal parts.
The length of the diagonals can be obtained using the Pythagoras theorem.
When the diagonals bifurcate each other, the angles at the center of a rectangle go one obtuse angle and the other an acute angle.
When two diagonals bisect each other at 90° it is chosen a square.

Are Diagonals of Rectangle Equal?

The diagonals of a rectangle bisect each other and are equal. Since a rectangle is a quadrilateral, all the angles are right angles. A rectangle is besides a parallelogram where the opposite sides are equal.

Do Diagonals of Rectangle Bisect at ninety°?

The diagonals of a rectangle bisect each other just non at xc degrees angle.

How to Make up one's mind the Expanse of Rectangle When Diagonal of Rectangle is Given?

We tin can calculate the expanse (A) of a rectangle when its diagonal (d) and length (fifty) is given using the formula, Area = l × √(d² - l²).

How to Observe the Length of Rectangle When The Diagonal of Rectangle is Given?

Nosotros can calculate the length of rectangle (l) when its diagonal (d) and width (w) is given using the formula, l = √(d² - w²).