5-1 Perpendicular and Angle Bisectors

1. 5-1Perpendicular and Angle Bisectors Anna Chang 10-1 / T2

2. What is perpendicular bisector? • Perpendicular bisector is a line that cuts a segment into two equal parts, it creates 90 degrees.

3. 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

4. Examples A 90 degrees B n is the perpendicular bisector of the segmen AB

5. 90 degrees ㄱ n is the perpendicular bisector of the segmen AB

6. n is the perpendicular bisector of XY 90 degrees

7. Q is the perpendicular bisector of OP 90 degrees

8. Perpendicular bisector theorem is … • If a point lies on the perpendicular bisector of a segment then it is equidistant from both of the endpoints of the segment. XA=XB

9. Examples Example 1 : AB andCB AB=CB 5z+23=6z+14 9=1z Z=9 5(9)+23 AB=68 6.6(9)+14 CB=68

10. Find X X=24 Since 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 CPCT So X=24

13. Converse of Perpedicular Bisector Theorem • A point lies on the perpendicular bisector of a segment if and only if is equidistant from both of the sides

14. Examples