Isosceles triangle is the triangle in which any two sides of the triangle are equal to each other. According to triangle properties, angles opposite to equal sides are also equal. This implies that in an isosceles triangle, when any two sides are equal in measure, then the angles opposite to those equal sides are also equal in measure. The angles in an isosceles triangle can be calculated using the sum of the angles formula, where all the three angles add up to 180º.
Example1: ABC is an isosceles triangle in which side AB is equal to side AC. If the measure of angle A is 80º, then what is the measure of the remaining two angles?
In triangle ABC, given sides AB = AC.
We know that, angles opposite to equal sides are also equal.
Angles opposite to sides AB and AC are B and C respectively.
Therefore, angle B= angle C= xº.
Sum of the angles in a triangle = 180º==> 80º+ x+ x= 180º
Hence, 80º+ 2x= 180º==> 2x= 180-80==> 2x= 100==>x= 50º.
Example 2: PQR is an isosceles triangle with sides, PQ = PR. If the perimeter of the triangle is 20m and the side length of QR is 8m, then what is the length of the remaining sides?
Let length of the side PQ = PR = x
Perimeter of a triangle = Sum of all the sides of the triangle
This gives: PQ + PR + QR = 20
So, x + x + 8= 20==> 2x+ 8 = 20
2x = 20- 8 ==>2x = 12==> x = 6m
Therefore, sides PQ= PR= 6m.