Triangle

See how to find the angles/sides/area of a triangle.
16 examples and their solutions.

Types of Triangles

Angles

Acute Triangle	Right Triangle	Obtuse Triangle

3 acute angles (0 < m∠ < 90)	1 right angle (m∠ = 90)	1 obtuse angle (90 < m∠ < 180)

Sides

Scalene Triangle	Isosceles Triangle	Equilateral Triangle

No congruent sides	2 congruent sides	3 congruent sides

Interior Angles of a Triangle

Formula

m∠1 + m∠2 + m∠3 = 180

Example

Solution

Exterior Angle of a Triangle

Formula

m∠1 = m∠2 + m∠3

Example

Solution

Example

Solution

Triangle Inequality Theorem

Theorem

a + b > c

The sides of a triangle satisfy this inequality.
a + b: Sum of the shorter sides
c: Longest side

Example

2, 3, 4
Can be the sides of a triangle?

Solution

Example

2, 7, 9
Can be the sides of a triangle?

Solution

Example

3, 4, 8
Can be the sides of a triangle?

Solution

Example

3, 5, 5
Can be the sides of a triangle?

Solution

Relationship between Sides and Angles of a Triangle

Example

Compare m∠A, m∠B, m∠C.

Solution

Example

Compare AB, AC, BC.

Solution

Example

Compare AB, AC, BC.

Solution

Isosceles Triangle

Definition

An isosceles triangle is a triangle
that has two congruent sides (= legs).
The non-congruent side is the base.
The two angles
that are adjacent to the base
are congruent.

Example

Solution

Example

Solution

Example

Solution

Area of a Triangle

Formula

A = 12bh

Example

Solution

Example

Solution

Example

Solution