5.1 Perpendicular Bisector Equidistant. Definition of a Perpendicular Bisector A Perpendicular Bisector is a ray, line, segment or even a plane that is.

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Presentation transcript:

5.1 Perpendicular Bisector Equidistant

Definition of a Perpendicular Bisector A Perpendicular Bisector is a ray, line, segment or even a plane that is perpendicular to a segment at its midpoint. AM = MB

Theorem about the perpendicular bisector If a point is on the perpendicular bisector of a segment, then it is an equal distance from the end points of the segment. EA = EB FA = FB GA = GB HA = HB

Converse If a point is an equal distance from the endpoints of a segment, then its on the perpendicular bisector.

Converse Is point T on line OP ? Why

Angle Bisector Theorem If a point is on the angle bisector, then it is an equal distance from the sides.

Converse of the Angle Bisector Theorem If a point is in the interior of an angle and it is an equal distance from the sides, then it is on the angle bisector.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Lets Prove it #1. R is on the bisector of #1. Given #2.#2.All Right #3.#3.Reflexive #4.#4. Def of bisector #5. #5. AAS #6. C.P.C.T.

Homework Page 268 – 269 #8, 10, 11, 12, 16, 17, 20, 21 – 26, 28, 30, 32