# Perpendicular Bisectors, Angle Bisectors, and Circumcenters

## Follow these steps to construct perpendicular bisectors

1) Using the COMPASS TOOL, create a circle with radius AB and center point A
2) Using the COMPASS TOOL, create a circle with radius AB and center point B
3) Using the SEGMENT TOOL, draw a segment that connects the intersections of circles A and B
4) Using the POINT TOOL, mark point E at the intersection of segments AB and CD

*RESULTS: Segment CD is the***Perpendicular Bisector**of segment AB Point E is the**Midpoint**of segment AB## Construction #1

## Check Your Understanding

What does the term perpendicular bisector mean?

## Follow these steps to bisect an angle:

1) Using the POINT TOOL, mark point D on segment AB
2) Using the COMPASS TOOL, create a circle with radius AD and center point A
3) Using the POINT TOOL, mark point F where circle A intersects segment AC
4) Using the COMPASS TOOL, create a circle with the radius DF and center point D
5) Using the COMPASS TOOL, create a circle with the radius DF and center point F
6) Using the SEGMENT TOOL, draw a segment from point A to the intersection of circles D and F

*RESULTS: Segment AG is the Angle Bisector of angle CAB*## Check Your Understanding

What does the term angle bisector mean?

## The Circumcenter of a Triangle

## Check Your Understanding

The circumcenter is the intersection of which 3 lines in a triangle?

## Think About It

If you needed to find the balancing point of a triangle, what would you do? Which steps would you take to find the balancing point (center of gravity)?