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5-1 Vocabulary Equidistant Locus
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5.1 Perpendicular and Angle Bisectors
Geometry
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Bisector l bisector –a line, seg,ray or plane that is to a segment at its midpoint. A pt is equidistant from 2 pts if it is the same distance from each pt. (don’t have to all be collinear) __ A _ B M
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Thm bisector thm If a pt is on the bisector of a segment then it is equidistant from the endpts of the segment. C l B A M If l is the bisector of seg AB then CA=CB (and DA=DB) D
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Thm 5-1-2 Converse of the bisector thm
If a pt is equidistant from the endpts of a segment then it is on the bisector C M B A If CA=CB then C is on the bisector of AB
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Ex. 1a) Find MN N M L Ex. 1a, b, c l
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Ex. 1b.) Find BC
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Ex. 1c.) Find TU
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Proof Statements 1. l is the bisector 2. M is the midpt of seg AB 3.
4. 5. 6. BCM Reasons 1. given 2. Def of bisector 3. Def of a midpt 4. bisector thm 5. Reflex prop of 6. SSS
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Distance from a pt to a line
Distance from a pt to a line- the length of the seg from the pt to the line. PD=distance from P to line l P l D
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Thm 5-1-3 bisector thm D A ) O ) G
If a pt is on the bisector of an then it is equidistant from the sides of the . D A ) O ) G
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Thm 5-1-4 converse of the bisector
If a pt is in the interior of an and is equidistant from the sides then it is on the bisector.
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Ex. 2 Additional Ex 2 a. b. c pg. 302
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Assignment
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