CK-12 Geometry-Concepts

http://www.ck12.org Chapter 5. Relationships with Triangles

Example B

IfJ,E, andGare midpoints andKA=AD=AHwhat are pointsAandBcalled?

Ais the incenter becauseKA=AD=AH, which means that it is equidistant to the sides. Bis the circumcenter

becauseJB,BE, andBGare the perpendicular bisectors to the sides.

Example C

−→

ABis the angle bisector of^6 CAD. Solve for the missing variable.

CB=BDby the Angle Bisector Theorem, so we can set up and solve an equation forx.

x+ 7 = 2 ( 3 x− 4 )

x+ 7 = 6 x− 8

15 = 5 x

x= 3

Watch this video for help with the Examples above.

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/52526

CK-12 Foundation: Chapter5AngleBisectorsB

Concept Problem Revisited

The airport needs to be equidistant to the three highways between the three cities. Therefore, the roads are all

perpendicular to each side and congruent. The airport should be located at the incenter of the triangle.