Triangles

Classifying triangles by sides and angles, the angle sum of a triangle, the exterior angle theorem and properties of isosceles and equilateral triangles.

Types of triangles

By sides

Scalene: no equal sides
Isosceles: two equal sides, and the two base angles are equal
Equilateral: three equal sides, all angles $60^\circ$

By angles

Acute: all angles less than $90^\circ$
Right: one angle $90^\circ$
Obtuse: one angle more than $90^\circ$

Two theorems

Example 1●●

An isosceles triangle has an apex angle of $40^\circ$. Find each base angle.

Base angles are equal: $2b + 40 = 180$.

$b = 70^\circ$

Example 2●●

The exterior angle at $C$ is $125^\circ$ and $\angle A = 48^\circ$. Find $\angle B$.

$\angle A + \angle B = 125^\circ$

Exterior angle of a triangle

$\angle B = 125 - 48 = 77^\circ$

Flashcards

Exterior angle theorem

Exterior angle = sum of the two opposite interior angles.

Isosceles triangle

Two equal sides, two equal base angles.

Equilateral triangle angles

$60^\circ$ each

Practice

An isosceles triangle has apex angle $40^\circ$. Find a base angle.
Exterior angle $125^\circ$, opposite interior angle $48^\circ$. Find the other opposite interior angle.
A triangle has angles $90^\circ$ and $35^\circ$. Find the third.
An isosceles triangle has base angles $40^\circ$. Find the apex angle.
A triangle with angles $30^\circ$, $50^\circ$, $100^\circ$ is:
A triangle has angles $x^\circ$, $2x^\circ$ and $3x^\circ$. Find $x$.
Find an exterior angle of an equilateral triangle.
Can a triangle have two obtuse angles?