In this page we practice identifying different types of triangles based on their angles and side lengths.

Example 1 – Acute Triangle

Angles: 70°, 60°, 50°

All angles are less than 90°, so this triangle is an acute triangle.

Example 2 – Right Triangle

Angles: 90°, 45°, 45°
Because one angle is 90°, this triangle is a right triangle.

Example 3 – Obtuse Triangle

Angles: 130°, 30°, 20°

One angle is greater than 90°, so this triangle is an obtuse triangle.

Example 4 – Scalene Triangle

Angles: 110°, 40°, 30°

All sides are different, which means all angles are different.
This triangle is a scalene triangle.

Example 5 – Isosceles Triangle

Two sides are equal.

Because the sides are equal, the angles opposite those sides are also equal.
This triangle is an isosceles triangle.

Example 6 – Equilateral Triangle

All three sides are equal.

Since the sum of the angles of a triangle is 180°, we can write:

x + x + x = 180°

3x = 180°

x = 60°

So an equilateral triangle has three 60° angles.

Triangle Inequality Examples

Can the following side lengths form a triangle?

1. 1, 2, 2 → True
   Because 1 + 2 > 2
2. 2, 2, 2 → True
   Because 2 + 2 > 2
3. 1, 1, 3 → False
   Because 1 + 1 < 3
4. 1, 2, 3 → False
   Because 1 + 2 = 3
5. 4, 5, 6 → True
   Because 4 + 5 > 6
6. 3, 3, 5 → True
   Because 3 + 3 > 5
7. 5, 9.5, 5 → True
   Because 5 + 5 > 9.5
8. 5, 9.9, 5 → True
   Because 5 + 5 > 9.9
9. 5, 5, 10 → False
   Because 5 + 5 = 10

When the sum of two sides equals the third side, the shape collapses into a straight line, so it is not a triangle.

Practice

• More Examples

• Take the Quiz

Continue Learning

1. Types of Triangles
2. Triangles (Basics)
3. Sum of Angles of a Triangle is 180° (Proof)
4. Find the Missing Angle of a Triangle
5. Sum of Exterior Angles of a Triangle (Proof)
6. Exterior Angle Theorem of a Triangle
7. Two Exterior Angles at a Vertex are Equal (Proof)
8. Two Exterior Angles are Equal at a Vertex (Quick Proof)

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