Chapter 5 Section 2Bisectors in Triangles

With your straight edge, draw line segment AB. Use your compass and straight edge to

draw the perpendicular bisector of AB. Label the point of intersection D, and label

one other point on the perpendicular bisector C.

A

C

B

Based on what you learned up to this point, what triangles can you draw from these points, and what can you say about their congruency?

D

Perpendicular Bisector Theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

D

E

F G

.,sec EGEDDGoftorbiaisEFIf

Converse of the Perpendicular Bisector Theorem: If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

D

E

F G

,sec, DGoftorbitheonisEEGEDIf

Example 1

D

E

F G

5H

EH is the perpendicular bisector of DG. Find DH and EG.

7

Can we say that DG is the perpendicular bisector of EH? Why or why not?

5

7

DH

EG

Distance from a point to a line is the length of the perpendicular segment from the point to the line.

A

C

B

Distan

ce fr

om a point t

o a lin

e,

Perp

endicu

lar to

the e

xterio

r angle

segm

ent…

Angle Bisector Theorem: If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.

A

C

B

Converse of the Angle Bisector Theorem: If a point in the interior of an angle is is equidistant from the sides of the angle, then the point is on the angle bisector.

A

C

B

D

.sec, AoftorbitheonisDDBCDIf

Converse of the Angle Bisector Theorem: If a point in the interior of an angle is is equidistant from the sides of the angle, then the point is on the angle bisector.

A

C

B

D

.sec, AoftorbitheonisDDBCDIf

What is the length of segment FD?

242 x

.2

x5

F

E

D

C

B

A

FDx

x

x

xx

40242

8

243

2425

x2

)20( xK

H

E

D

10

How far is K from EH?How far is K from ED?What can you conclude about EK?Find measure of angle DEH.

.3

Geometry Classwork - Page 267: 2,4,6-15, 18-25.When you are done with classwork, have it checked, then proceed to Homework.

Geometry Homework (Due Mon after Thanksgiving break) Perpendicular and Angle Bisectors: 1-8, 11-30