Equilateral Triangles, Isosceles Triangles and Scalene Triangles

This lesson reviews the common types of triangles in geometry.

Triangles are three-sided shapes that lie in one plane. Triangles are a type of polygons. The sum of all the angles in any triangle is 180º.

Triangles can be classified according to the size of its angles. Some examples are right triangles, acute triangles and obtuse triangles.

The lengths of the sides of triangles is another common classification for types of triangles. Some examples are equilateral triangles, isosceles triangles and scalene triangles.

Equilateral Triangles

An equilateral triangle has all three sides equal in length. Its three angles are also equal and they are each 60º.

Example 1: An equilateral triangle has one side that measures 5 in. What is the size of the angle opposite that side?

Solution:

Step 1: Since it is an equilateral triangle all its angles would be 60º. The size of the angle does not depend on the length of the side.

Answer: The size of the angle is 60º.

Isosceles Triangles

An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal.

Example 1: An isosceles triangle has one angle of 96º. What are the sizes of the other two angles?

Solution:

Step 1: Since it is an isosceles triangle it will have two equal angles. The given 96º angle cannot be one of the equal pair because a triangle cannot have two obtuse angles..

Step 2: Let x be one of the two equal angles. The sum of all the angles in any triangle is 180°. 
      x + x + 96° = 180° Þ 2x = 84° Þ x = 42°

Answer: The sizes of the other two angles are 42º each.

Example 2: A right triangle has one other angle that is 45º. Besides being right triangle what type of triangle is this?

Solution:

Step 1: Since it is right triangle it will have one 90º angle. The other angle is given as 45º.

Step 2: Let x be third angle. The sum of all the angles in any triangle is 180º.
      x + 90º + 45º = 180° Þ x = 45º

Step 3: Two of the angles are equal which means that it is an isosceles triangle.

Answer: It is also an isosceles triangle.

Scalene Triangles

A scalene triangle has no sides of equal length. Its angles are also all different in size.

The following videos shows the different types of triangles and some problems involving the angles.

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