Perpendicular and Angle Bisectors

Learn and apply perpendicular and angle bisectors.

Lesson 5 of 53 parts Practice Flashcards

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Perpendicular Bisectors

Objective: Apply perpendicular bisectors in triangle problems.

A point on a segment’s perpendicular bisector is equidistant from its endpoints.

Point P on the perpendicular bisector of AB is the same distance from A and from B.

Worked examples

Try itPoint P1 lies on the perpendicular bisector of AB, with PA = 6. Find PB.Show answer

6. A point on a perpendicular bisector is equidistant from the endpoints.

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Perpendicular Bisectors

Objective: Apply perpendicular bisectors in triangle problems.

A point on a segment’s perpendicular bisector is equidistant from its endpoints.

Worked examples

Try itPoint P1 lies on the perpendicular bisector of AB, with PA = 6. Find PB.Show answer

6. A point on a perpendicular bisector is equidistant from the endpoints.

Angle Bisectors

Objective: Apply angle bisectors in triangle problems.

A point inside an angle on its bisector is equally distant from the sides, using perpendicular distances.

Point P on the bisector of an angle has equal perpendicular distances to the two sides.

Worked examples

Try itPoint Q1 lies inside an angle on its bisector. Its perpendicular distance to one side is 4. What is its perpendicular distance to the other side?Show answer

4. A point on an angle bisector is equally distant from the two sides.

Equidistance Applications

Objective: Apply equidistance applications in triangle problems.

Equal endpoint distances locate points on a perpendicular bisector; equal side distances inside an angle locate points on its bisector.

Worked examples

Try itPoint R1 is equally distant from endpoints A and B. Which locus contains R1?Show answer

The perpendicular bisector of AB. The converse perpendicular-bisector theorem locates points equidistant from A and B.

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