Perpendicular Bisectors & Angle Bisectors

Front

A ray that divides an angle into two congruent angles is called .............

Back

angle bisector

Front

What is the definition of a perpendicular bisector?

Back

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

Front

If a point lies on the perpendicular bisector of a segment, what can be said about its distance to the endpoints of the segment?

Back

It is equidistant from both endpoints.

Front

What is the relationship between angle bisectors and the angles they divide?

Back

Angle bisectors create two angles that are congruent.

Front

In triangle geometry, what is the significance of the incenter?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is the center of the inscribed circle.

Front

If the measure of angle A is 60 degrees, what is the measure of each angle created by the angle bisector of angle A?

Back

30 degrees each.

Front

What is the formula for finding the length of a segment created by a perpendicular bisector in a right triangle?

Back

The length can be found using the Pythagorean theorem.

Front

If a triangle has sides of lengths 6, 8, and 10, what is the length of the angle bisector from the vertex opposite the longest side?

Back

The length of the angle bisector can be calculated using the angle bisector theorem.

Front

What is the angle bisector theorem?

Back

It states that the ratio of the lengths of the two segments created by the angle bisector is equal to the ratio of the lengths of the other two sides of the triangle.

Front

If the angle bisector divides an angle of 80 degrees, what are the measures of the two angles formed?

Back

40 degrees each.