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:
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 nonequal 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:
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^2a^{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