Perpendicular Bisector Theorem and Angle Bisector Theorem

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

Define an Angle Bisector.

Back

An Angle Bisector is a line, ray, or segment that divides an angle into two equal parts.

Front

What does the Reflexive Property of Congruence state?

Back

The Reflexive Property of Congruence states that any geometric figure is congruent to itself.

Front

What is the Triangle Angle Bisector Theorem?

Back

The Triangle Angle Bisector Theorem states that the ratio of the lengths of the two segments created by an angle bisector on the opposite side is equal to the ratio of the lengths of the other two sides of the triangle.

Front

What is a Midpoint?

Back

A Midpoint is a point that divides a segment into two congruent segments.

Front

What is a Perpendicular Bisector?

Back

A Perpendicular Bisector is a segment, line, or ray that intersects another segment at its midpoint and forms a right angle (90 degrees) with it.

Front

If a point lies on the angle bisector of an angle, what can be said about its distances to the sides of the angle?

Back

The distances from the point to the sides of the angle are equal.

Front

How do you find the length of a segment using the Midpoint Formula?

Back

Front

What is the relationship between the segments created by an angle bisector in a triangle?

Back

The segments created by an angle bisector are proportional to the lengths of the other two sides of the triangle.

Front

What is the significance of the Perpendicular Bisector in triangle construction?

Back

The Perpendicular Bisector can be used to find the circumcenter of a triangle, which is the point where the three perpendicular bisectors intersect.