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Isosceles Triangle

A triangle is a plane that is surrounded by three lines.

We have three types of triangles, when we classify them on the basis of sides as follows:

  • Equilateral triangles
  • Isosceles triangles
  • Scalene triangles. 

Let us discuss in detail about isosceles triangle.

Isosceles Triangle:
An isosceles triangle has two sides equal. It also has two angles identical. In an isosceles triangle, the angles that are corresponding to equal sides are equal. 

A triangle which has two sides and two angles identical, is known as an isosceles triangle. 

Following figure shows an isosceles triangle:

Isosceles Triangle

Properties of Isosceles Triangles:

Isosceles triangles possess the following properties.
  • Two sides of an isosceles triangle are equal.
  • Internal angles corresponding to equal sides in an isosceles triangle are equal.
  • When in an isosceles triangle, the third angle (other than equal angles) is $90^{\circ}$, the triangle is referred as "right isosceles triangle".
  • The perpendicular drawn from vertex opposite to third non-equal side (also known as altitude) bisects the third side as well as bisects the angle between equal sides.
Area of Isosceles Triangle:
Let us consider a $\bigtriangleup$ABC in which AB = AC = b, BC = a and altitude AD = h as shown in the following figure:
Area of Isosceles Triangle
We know that the formula for area of a triangle is Area = $\frac{1}{2}$ x base x height

Here, Base = a

Height h = $\sqrt{b^2-(\frac{a}{2})^{2}}$

h = $\sqrt{b^2-\frac{a^{2}}{4}}$

Substituting these values in the above formula of area, we get

Area of isosceles triangle = $\frac{1}{2}$$ \times a \times \sqrt{b^2-\frac{a^{2}}{4}}$

Therefore, we have the following formula for area of an isosceles triangle.

Area of isosceles triangle = $\frac{a}{4}$$\sqrt{4b^2-a^{2}}$

Perimeter of Isosceles Triangle:
The perimeter of an isosceles triangle described in the above figure is given by the following formula:

Perimeter  = a + 2b

Related Calculators
Calculate Isosceles Triangle Isosceles Trapezoid Calculator
Area of Triangle Triangle Calculator
 

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