# Angle Bisectors of Triangles

## What is an Angle Bisector? An angle bisector is a line that divides an angle into two equal parts. It is a line that goes from one side of the angle to the other, cutting the angle into two equal halves. The two halves of the angle should have the same measure. In geometry, angle bisectors are used to divide the angles of a triangle into two equal halves.

## The 8.2 Angle Bisector Theorem The 8.2 Angle Bisector Theorem states that if a line is drawn from a vertex of a triangle to the midpoint of the opposite side, then the line will bisect the angle at the vertex. This means that the angle at the vertex is divided into two equal angles, each having a measure of half the angle’s original measure. This theorem can be used to find the measure of an angle in a triangle when you know the measurements of the other two angles.

## How to Use the 8.2 Angle Bisector Theorem To use the 8.2 Angle Bisector Theorem, you need to draw a line from one vertex of the triangle to the midpoint of the opposite side. Then you can use the measurements of the other two angles to calculate the measure of the angle at the vertex. For example, if you have two angles with measurements of 40° and 50°, you can use the 8.2 Angle Bisector Theorem to calculate the measure of the third angle. You would draw a line from the vertex to the midpoint of the opposite side, and then you would use the two known angles to calculate the measure of the third angle. The third angle would have a measure of 90°, half of the sum of the other two angles.

## Applications of the 8.2 Angle Bisector Theorem The 8.2 Angle Bisector Theorem can be used in many different ways. It can be used to calculate the measure of an angle in a triangle when you know the measurements of the other two angles. It can also be used to find the lengths of the sides of a triangle when you know the measures of two angles and the length of the opposite side. This theorem can also be used to prove the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

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The 8.2 Angle Bisector Theorem is a useful tool in geometry that can be used to find the measure of an angle in a triangle when you know the measurements of the other two angles. It can also be used to find the lengths of the sides of a triangle when you know the measures of two angles and the length of the opposite side. This theorem can also be used to prove the Triangle Inequality Theorem. Knowing the 8.2 Angle Bisector Theorem can be very helpful in geometry and can help you solve many different types of problems.