5-1 Vocabulary Equidistant Locus

5.1 Perpendicular and Angle Bisectors Geometry

 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

Thm 5-1-1  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

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

Ex. 1a) Find MN N M L Ex. 1a, b, c l

Ex. 1b.) Find BC

Ex. 1c.) Find TU

Proof Statements 1. l is the  bisector 2. M is the midpt of seg AB 3. 4. 5. 6.  ACM @  BCM Reasons 1. given 2. Def of  bisector 3. Def of a midpt 4.  bisector thm 5. Reflex prop of seg @ 6. SSS

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

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

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.

Ex. 2 Additional Ex 2 a. b. c pg. 302

Assignment