Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

What is an angle bisector?

Back

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

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 angle bisector divides the angle into two equal parts.

Front

What is the relationship between perpendicular bisectors and triangles?

Back

The perpendicular bisectors of the sides of a triangle intersect at a point called the circumcenter, which is equidistant from the vertices of the triangle.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is the center of the circumcircle, the circle that passes through all three vertices of the triangle.

Front

How can you determine if two segments are congruent using angle bisectors?

Back

If two angles are bisected and the segments opposite the angles are equal, then the segments are congruent.

Front

What is the measure of an angle if its bisector creates two angles of 23 degrees each?

Back

The measure of the original angle is 46 degrees.

Front

What is the formula for finding the length of a segment when given the coordinates of its endpoints?

Back

The length of a segment can be found using the distance formula: d = √((x2 - x1)² + (y2 - y1)²).

Front

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

Back

The angles formed by a perpendicular bisector and the original segment are right angles (90 degrees).

Front

How do you find the length of a segment if you know the coordinates of its endpoints?

Back

Use the distance formula: d = √((x2 - x1)² + (y2 - y1)²).