# Acute Triangle

By the end of this lesson, you will be able to

- define acute triangle.
- classify different types of acute triangle.
- interpret properties of acute triangle.
- demonstrate examples of acute triangle.

## Acute Angle

An angle of less than 90° is called an acute angle.

An acute angle

An Acute Triangle

## Acute Triangle

An acute triangle is a triangle in which all three angles are acute.

In acute triangle, the sum of any two angles is always greater than 90^{0}

The sides of an acute triangle may be same or different in measuring.

The intersection of three perpenduculars drawn from the vetices to respective opposite sides is an interior point in an acute triangle.

Thus, orthocenter and circumcenter are the interior points for an acute triangle.

### Acute Triangle Example

## Types of Acute Triangle

Acute triangle is divided into the following:

- Acute Scalene Triangle
- Acute Isosceles Triangle
- Acute Equilateral Triangle

### Acute Scalene Triangle

An Acute scalene triangle is a triangle in which all three angles are different measuring and each of less than 90°.

An acute scalene triangle

An acute scalene triangle is showing its unequal sides.

All three angles are different in measure implies that all three sides of an acute scalene triangle are also different in length.

### Acute Isosceles Triangle

An Acute isosceles triangle is an acute triangle with two equal acute angles.

An acute isosceles triangle

This is an acute isosceles triangle because it has two equal sides mentioned.

As a result, the two acute angles, opposites of two equal sides are also equal.

### Acute Equilateral Triangle

An acute equilateral triangle is a triangle in which all three angles are acute and equal; and each equal acute angle is exactly 60°.

An acute equilateral triangle

Every equilateral triangle is formed with three equal sides. As a result, each of its acute angle, opposite of the three equal sides, is also equal to 60°.

Hence, every equilateral triangle is an acute equilateral triangle.