Angle Bisectors

Front

What is an angle bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

If an angle measures 130 degrees, what is the measure of each angle formed by its bisector?

Back

Each angle formed by the bisector would measure 65 degrees.

Front

How do you find the measure of an angle when given its bisector?

Back

To find the measure of an angle when given its bisector, you can use the property that the bisector divides the angle into two equal parts.

Front

What is the relationship between the angles formed by a bisector and the original angle?

Back

The angles formed by a bisector are equal to each other and each is half of the original angle.

Front

If \\overrightarrow{BD} bisects \\angle ABC and m\\angle ABC = 80 degrees, what is m\\angle ABD?

Back

m\\angle ABD = 40 degrees.

Front

What is the formula to find the measure of an angle when given the measures of the two angles formed by its bisector?

Back

The measure of the original angle is the sum of the measures of the two angles formed by the bisector.

Front

If \\overrightarrow{QS} bisects \\angle PQR and m\\angle PQR = 104 degrees, what is m\\angle PQS?

Back

m\\angle PQS = 52 degrees.

Front

In a triangle, if one angle measures 60 degrees and is bisected, what are the measures of the two resulting angles?

Back

Each resulting angle measures 30 degrees.

Front

What is the significance of angle bisectors in triangle geometry?

Back

Angle bisectors are significant because they help in finding the incenter of a triangle, which is the point where the angle bisectors intersect.

Front

How can angle bisectors be used to solve for unknown variables in geometric problems?

Back

Angle bisectors can be used to set up equations based on the property that they divide angles into equal parts, allowing for the solution of unknown variables.