Isosceles Triangle
Isosceles Triangle is one of the special type of the triangle. In an isosceles triangle, the length of two sides are equal and the measure of two angles are equal.
In the above shown figure, the length of AC and BC are equal. i.e, a = c. And also, L A = L B. Therefore, the triangle ABC is an isosceles triangle.
The perimeter of an isosceles triangle is given by the formula, P = 2a + b, where P is the perimeter, a is the length of the side BC and b is the length of the side AC.
The semi perimeter of an isosceles triangle is given by the formula, S = a + b/2, where, S is the semi perimeter, a is the length of the side BC and b is the length of the side AC.
The area of the isosceles triangle is given by the formula, A = `b(sqrt(4a^(2)-b^(2)))/(4)` , where a is the length of the side BC and b is the length of the side AC.
There are two different types of isosceles triangle based on the measure of the angles. They are:
- Isosceles Acute Triangle
- Isosceles Obtuse Triangle
Isosceles Acute Triangle is a triangle in which the measure of every angle is less than 90 degrees. And also, two sides are equal in length and two angles are equal in measurement.
Isosceles Obtuse Triangle is a triangle in which the measure of every angle is greater than 90 degrees. And also, two sides are equal in length and two angles are equal in measurement.
Below are some example problems on isosceles triangle
Example Problem 1: The isosceles triangle has base length 13 cm and 10 cm.Find the area of the isosceles triangle.
Solution: Given: Base length (b) = 13 cm
Height (h) = 10 cm
Formula: Area of isosceles triangle (A) = `1/2` base x height square units
= `1/2` x 13 x 10
= `1/2` x 130
= `"130 / `
= 65
Area of the isosceles triangle (A) = 65 cm2
Example Problem 2: Find the perimeter of isosceles triangle whose sides are 8.5 cm and 6 cm.
Solution: Given: b = 8.5 cm
a = 6 cm
Formula: Perimeter of isosceles triangle (P) = a + b + b units
= 8.5 + 8.5 + 6
Perimeter of isosceles triangle (P) = 23 cm
ABC is a triangle, the bisector of 
meets AB at X. A point Y lies on CX such that AX = AY. Prove that 
and AX = AY.
