Ximpledu

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