Isosceles Triangle

An isosceles triangle is a triangle which has any two of its sides equal to each other. Also, the angles opposite these equal sides are equal. In general, a triangle is a polygon which has three sides and three vertices. The sides and angles of triangle could vary. The types of triangles can be classified based on the sides and angles. Based on the sides, a triangle is classified into three types namely: Scalene, Isosceles and Equilateral. Whereas based on the angles, a triangle is classified into three types namely: Acute Angled, Obtuse Angled and Right Angled.

Table of contents:

Isosceles Triangle Definition

An Isosceles triangle is a triangle which has two equal sides. Also, the two angles opposite to the two equal sides are equal. Suppose in a triangle △ABC, if sides AB and AC are equal, then △ ABC is an isosceles triangle where ∠ B = ∠ C.

Isosceles Triangle

The triangle having all the three sides equal is called an Equilateral triangle. Also, the triangle having all the three unequal sides is called a Scalene triangle.

Isosceles Triangle Properties

  1. As the two sides are equal in this triangle, the unequal side is called the base of the triangle.
  2. The angles opposite to the two equal sides of the triangle is always equal.
  3. The altitude of an isosceles triangle is measured from the base to the vertex(topmost ) of the triangle.
  4. A right isosceles triangle has the third angle as 90 degrees.

What is Right Isosceles Triangle?

A right isosceles triangle has two equal sides, wherein one of the two equal sides act as perpendicular and another one as a base of the triangle. The third side, which is unequal, is termed as the hypotenuse. Therefore, we can apply here the famous Pythagoras theorem, where the square of the hypotenuse is equal to the sum of the square of base and perpendicular.

Suppose, the sides of the right isosceles triangle are a, a, and h, where a  is the two equal sides and h is the hypotenuse, then;

h = √(a2 + a2) = √2a2 = a√2

or h = √2 a

Also, read:

Isosceles Triangle Area Formula

The area of an isosceles triangle is = ½ × b × h, where b is the base and h is the height of the triangle.

A = ½ × b × h

Isosceles Triangle Perimeter Formula

As we know the perimeter of any shape is the boundary of the shape. Similarly, the perimeter of an isosceles triangle can be found if we know its base and side.

P = 2a + b, where ‘a’ are the two equal sides of the triangle and b is the base of the triangle.

Examples

Example 1: Find the area of an isosceles triangle given its height as 6 cm and base as 4 cm?

Solution: Area of an isosceles triangle is ½ × b × h

A = ½ × 4 × 6 = 12 cm2

Example 2: Find the perimeter of an isosceles triangle, with side 6 cm and base 4 cm.

Solution : P = 2a + b = 2(6) + 4 = 12 + 4 = 16 cm

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