5.2 Use ⊥ Bisectors Mrs. vazquez Geometry.

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Presentation transcript:

5.2 Use ⊥ Bisectors Mrs. vazquez Geometry

g-Co.3.9, 4.12 ; g-c.1.3 Essential Question: How can ⊥ bisectors be used in ∆?s? Objective: Students will be use ⊥ bisectors to solve problems.

⊥ bisector theorem In a plane, if a point is on the ⊥ bisector of a segment, then it is equidistant from the endpoints of the segment. If CD is the ⊥ bisector of AB, then CA=CB.

converse of ⊥ bisector theorem In a plane, if a point is equidistant from the endpoints of a segment, then it is on the ⊥ bisector of a segment. If DA=BD, then D lies on the ⊥ bisector of AB.

Solve for x 1.Find NK. 2.Why is M on JK? N ∆NLK is isosceles K M J L MN≅ML; MN=8; JK bisects NL LK = 4x+1; NK = 6x-5 1.Find NK. 2.Why is M on JK?

Vocab Concurrent: when 3+ lines, rays, or segments intersect in the same point

Vocab Circumcenter: the point of concurrency of the three ⊥ bisectors of a ∆.

concurrency of ⊥ bisectors of a ∆ The ⊥ bisectors of a ∆ intersect at a point that is equidistant from the vertices of the ∆. If GE, GF, & GD are ⊥ bisectors, then GA=GB=GC.

real-life Application Ice cream is sold at three points around the park. Dylan is standing equidistant to all three vendors. Where could he be standing?