5.3 Use ∡ Bisectors of ∆s Mrs. Vazquez Geometry.

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Presentation transcript:

5.3 Use ∡ Bisectors of ∆s Mrs. Vazquez Geometry

g-Co.3.10, g-c.1.3 Essential Question: How can ∡ bisectors be used in ∆?s? Objective: Students will be use ∡ bisectors to find distance relationships.

∡ bisector theorem If a point on the bisector of an ∡, then it is equidistant from the two sides of the ∡. If BD bisects ∡ABC & ED⊥AB & FD⊥CB, then ED=FD.

Converse of the ∡ bisector theorem If a point is in the interior of an ∡ and is equidistant from the sides of an ∡, then it lies on the bisector of the ∡. If ED⊥AB & FD⊥CB & ED=FD, then BD bisects ∡ABC.

Solve for BD

Solve for BD

incenter the point of concurrency of ∡ bisectors

concurrency of ∡ bisectors theorem The ∡ bisectors of a ∆ intersect at a point that is equidistant from the sides of the ∆. If AP, BP, & CP are ∡ bisectors of ∆ABC, then PD=PE=PF.

Find YC ZP = 4x - 1 XP = x + 2 CP = 4x + 1