Isosceles Right Triangle is the one which has:**(a) One 90 degree angle****(b) Two sides of equal length**

As the name suggests Isosceles Right Triangle has** features of both right triangle and Isosceles Triangle**

**Isosceles Right Triangle Examples****Example 01**

Given above is the Right Angled Isosceles Triangle.

Notice the following features:

(a) Angle B measures 90 degree

(b) Two sides AB & BC are equal

AB = BC = 4 cms

**Example 02**

Triangle ABC is a Isosceles Right Triangle, where:

(a) Angle A measures exactly 90 degrees

(b) Side AB & AC are equal

AB = AC = 5 cms

**Structure of Isosceles Right Triangle**

Below is triangle ABC with sides AB = BC and angle B = 90

Isosceles Right Triangle consists of following components**(a) Hypotenuse**

The longest side of the triangle is known as Hypotenuse

Here side AC is the hypotenuse

**(b) Base**

The side placed horizontally is called base**(c) Height**

The line perpendicular to the base is called Height

Note

The sides Base and Height are at 90 degree with each other

**Properties of Right Isosceles Triangle**

**(01) The side opposite to 90 degree angle is the longest**

Because 90 degree is the largest angle in right isosceles triangle, its opposite will be the longest.

This longest side is also called Hypotenuse

**(02) The two equal sides also have equal angles whose value is 45 degree**

Given above is Right Isosceles Triangle with sides AB = BC

Since both sides are equal, the opposite angles are also equal.

Hence, \angle A =\angle C

**Proof**

The other two angles of Right Isosceles triangle measure 45 degree each

We know that:

\angle B = 90 degree

Let \angle A =\angle C =x

Using Angle property of Triangle

∠A + ∠B +∠C = 180

x + 90 + x = 180

2x = 90

x = 45 degree

Hence, Let \angle A =\angle C =45 degree

**(03) Location of Circumcenter, Centroid and Orthocenter**

All the points, circumcenter, Centroid and Orthocenter are located inside the triangle

**Area of Right Isosceles Triangle**

ABC is Right Isosceles Triangle where:

Base = Height = x cm

We know that:

Area=\ \frac{1}{2} \times \ base\ \times height

Area\ =\frac{1}{2} \ \times \ x\ \times x\\\ \\ Area=\ \frac{x^{2}}{2}

**Frequently asked Question – Right Isosceles Triangle**

**(01) Is Right Triangle and Right Isosceles Triangle the same thing?**

Just a small difference.

In Right Isosceles Triangle, the two sides are equal to each other while in Right Triangle all sides can have different length.

**(02) Can Right Isosceles triangle have Obtuse angle?**

NO!!!

Right Isosceles Triangle has one 90 degree angle and two 45 degree angle

**(03) What is the Perimeter of Right Isosceles Triangle?**

Read Solution

Perimeter can be calculated by adding all the sides

In the above right isosceles triangle, the perimeter can be calculated as:

Perimeter = x + x + a

Perimeter = 2x + a