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# 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

Solution

m∠1 = m∠2 + m∠3

Solution

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.

Solution

Solution

Solution

A = 12bh

Solution

Solution

Solution