5-1 Perpendicular and Angle Bisectors

Anna Chang10-1 / T2

5-1Perpendicular and Angle

Bisectors

Perpendicular bisector is a line that cuts a segment into two equal parts, it creates 90 degrees.

What is perpendicular bisector?

Here’s a segment AB N is the perpendicular bisector of segment AB

b/c n is the perpendicular bisector, then it creates a 90 degree angle

Examples

AB

90 degrees

n is the perpendicular bisector of the segmen AB

ㄱ 90 degrees

n is the perpendicular bisector of the segmen AB

90 degrees

n is the perpendicular bisector of XY

90 degrees

Q is the perpendicular bisector of OP

If a point lies on the perpendicular bisector of a segment then it is equidistant from both of the endpoints of the segment.

Perpendicular bisector theorem is …

XA=XB

ExamplesExample 1 : AB and CB1. AB=CB2. 5z+23=6z+143. 9=1z4. Z=95. 5(9)+23

AB=686.6(9)+14

CB=68

Find XX=24Since l is perpendicular bisector of TU, W is the midpoint of TU. <TWV and <WUV are right angles by def. of perpendicular. Later WV=VW by reflexive property. VT=VU by CPCTSoX=24

A point lies on the perpendicular bisector of a segment if and only if is equidistant from both of the sides

Converse of Perpedicular Bisector Theorem

Examples