Table of Contents
Angle Sum Property of a Triangle
A triangle has three angles, and the sum of the angles is always 180 degrees. This is called the angle sum property of a triangle. It is a very important property of triangles, because it can be used to figure out the angles of a triangle if you know two of them.
This property can also be used to determine whether or not a triangle is right angled. If all of the angles of a triangle add up to 90 degrees, then the triangle is right angled. This is because a right angled triangle has one angle that is 90 degrees.
Interior Angle Sum Property of Triangle
The interior angle sum property of triangle states that the sum of the interior angles of a triangle is 180 degrees. This is because a triangle is formed by three line segments, and the sum of the angles on a line segment is 180 degrees.
Exterior Angle Property of Triangle
The exterior angle property of a triangle states that the sum of the exterior angles of a triangle is equal to 180 degrees. This property can be proven using basic geometry. First, draw a triangle and label the angles A, B, and C. Next, draw lines from each vertex of the triangle to the opposite side. Finally, measure the angles created by these lines.
Angle A is the angle between the line from vertex A to side BC and the line from vertex A to side AC. Angle B is the angle between the line from vertex B to side AC and the line from vertex B to side BC. Angle C is the angle between the line from vertex C to side BC and the line from vertex C to side AC.
Since each angle is measured, it is clear that the sum of the angles is 180 degrees. This proves the exterior angle property of a triangle.
