Isosceles Triangle

Isosceles triangle is a three sided closed polygon with two equal sides and two equal angles.

Propeties of an isosceles triangle:

The legs are equal in the length and the third side is the base of the triangle.
The angles formed in the base side are equal in measures.i.e. they they are congruent to each other.
The angle formed by two legs of the triangle is vertex angle.

geometry isoscles triangle

Formula related related to isosceles triangle:

1. Formula to find the vertex angle of the isosceles triangle is

Sum of the angles in triangle is 180 degrees.

Here the base angle is equal.

a+a+ vertex angle= 180

Vertex angle = 180-2a.

2.Formula for the area of the isosceles triangle is `1/2 (BH)` square.units.

3.Formula for the perimeter of the isosceles triangle is sum of three sides.

Model problems to isosceles triangle

Pro 1: Find the vertex angle of the triangle whose base angle is 70 degrees?

Sol: Step 1:   Let the base angle be 70 degrees

We know that the base angles in the isosceles traingle is equal

Step 2:  Sum of the angles in triangle is 180 degrees.

Angle 1+ Angle 2+ Angle 3 = 180 degrees

x + x + vertex angle = 180

Step 3:   Vertex angle= 180- (140)

Vertex angle is 40 degrees

Vertex angle of the geometry isosceles triangle is 40 degrees.

Pro 2. Find the area of the isosceles triangle whose base side is 10cm and the height of the triangle is 3 cm.

Sol:  Step 1:   Base side, B= 10cm

Height of the triangle, H= 3cm

Step 2:  Formula for the area of the isosceles triangle is 1/2 (BH) square.units.

= `(1/2) (10 xx3)`

= `(30/2)`

= 15cm2

Area of the isosceles triangle = 15cm2

Pro 3: Find the perimeter of the isosceles triangle whose base side is 10cm and leg side is 5cm?

Sol: Step 1: We know that leg sides are equal in length.

Perimeter of the isosceles triangle  = (10+5+5)

= 20 cm

Perimeter of the isosceles triangle is 20cm