Table of Contents

Last modified on August 3rd, 2023

Isosceles triangle is a figure where two sides are of equal length and two angles are equal.

- Two equal (congruent) sides; in ∆ABC, AB and AC are two congruent sides
- One line of symmetry
- The two angles opposite to the equal sides are equal (isosceles triangle base angle theorem). In ∆ABC, since AB = AC, ∠ABC = ∠ACB
- The Altitude, AE bisects the base and the apex angle into two equal parts, forming two congruent right-angled triangles, ∆AEB and ∆AEC

Isosceles triangles are classified into three types: 1) acute isosceles triangle, 2) obtuse isosceles triangle, and 3) right isosceles triangles.

The differences between the types are given below:

**Area (****A****) = ½ (****b**** × ****h****)**, where b = base and h= height

**Problem:** Finding the area of an isosceles triangle when only ** THREE SIDES** are known

**Find the area of an isosceles triangle whose three sides measure 5 cm, 5 cm, and 6 cm**

Solution:

Here we will use the Pythagoras theorem to calculate the height of the triangle,

(**hypotenuse)**^{2 }**= (height)**^{2 }**+ (base)**^{2 }

Let, *a* = hypotenuse,

*b* = base,

*h* = height

The equation becomes,*h* = √*a*^{2} – (*b*/2)^{2}

In this triangle, *a* = 5 cm, *b* = 6 cm

Hence, *h* = √5^{2} – (6/2)^{2 }cm

= √ 25 – 9 cm

= 4 cm

Now, **A**** = ½ (****b**** x ****h****)**

= ½ (6 x 4) cm^{2}

= 12 cm^{2}

We know, **P**** = ****a****+ ****b**** +*** c*, where a, b, c are the measures of three sides

Since in an isosceles triangle two sides are equal i.e., *a* = *c*

Hence, **P**** = ****2a**** + ****b**

Last modified on August 3rd, 2023