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Obtuse Triangle

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

• define obtuse angle and obtuse triangle.
• classify different types of obtuse triangle.
• relate obtuse scalene triangle and obtuse isosceles triangle to obtuse triangle.
• demonstrate examples of obtuse triangle.

Obtuse Angle

An angle of greater than 90° and less than 180° is called obtuse angle.

There can have at best one obtuse angle in a triangle.

An obtuse angle is shown in figure.

An obtuse triangle is shown in figure.

obtuse Triangle

An obtuse triangle is a triangle that has one obtuse angle.

The sum of three interior angles is 180°.

So, an obtuse triangle cannot have more than one obtuse angle.

Therefore, an obtuse triangle must have one obtuse angle and two acute angles.

The side, opposite of obtuse angle, is always greater than each of other two.

Obtuse Triangle Example

An obtuse triangle

Types of Obtuse Triangle

There are two types of obtuse triangle in terms of side.

• Obtuse Scalene Triangle
• Obtuse Isosceles Triangle

Obtuse Scalene Triangle

An obtuse scalene triangle is a triangle that has one obtuse angle and other two acute angles.

An obtuse scalene triangle

It is an obtuse triangle whose two acute angles are unequal to each other.

consequently, two opposite sides of acute angles are also unequal. Therefore, it is an obtuse scalene triangle.

Again, every obtuse scalene triangle is also an scalene triangle

Obtuse Isosceles Triangle

A triangle with one obtuse angle and other two equal acute angles is an obtuse isosceles triangle.

An obtuse isosceles triangle

Here two acute angles are equal.

so the two sides, opposite of two acute angles, are always equal.

Therefore, an obtuse isosceles triangle is always an isosceles triangle.