The Isosceles Triangle

Mathematics — Second Preparatory

The Isosceles Triangle

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	In an isosceles triangle the vertex angle measures 40°. Find the base angles	isoscelestrianglevertexangle
Solution	The base angles are equal and the three angles add up to 180° so each base angle = (180 − 40) ÷ 2 = 70°. Check: 40 + 70 + 70 = 180	baseanglesequalthree
Example 2	In an isosceles triangle one base angle measures 65°. Find the vertex angle	isoscelestrianglebaseangle
Solution	The vertex angle = 180 − 65 − 65 = 50°	vertexangle
Example 3	An isosceles triangle has legs of (x + 3) cm each and a base of (x − 1) cm. Its perimeter is 26 cm. Find x then the side lengths	isoscelestrianglelegsbase
Solution	Perimeter = 2(x + 3) + (x − 1) = 3x + 5 = 26 so 3x = 21 and x = 7. The legs are 10 cm each and the base is 6 cm. Check: 10 + 10 + 6 = 26	PerimeterlegsbaseCheck

Key points

Example 4An isosceles triangle has legs of 10 cm and a base of 12 cm. Find the altitude drawn from the vertex to the base.

SolutionThe altitude bisects the base, so half the base is 6 cm. By the Pythagorean theorem, the altitude = √(10² − 6²) = √(100 − 36) = √64 = 8 cm.

The Isosceles Triangle · 3 / 5