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?

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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

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What does the term angle bisector mean?

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The Circumcenter of a Triangle

The Circumcenter of a Triangle
The center of a triangle's circumcircle. It is where the "perpendicular bisectors" (lines that are at right angles to the midpoint of each side) meet.
[color=#222222][size=100][size=150]The circumcenter of a triangle can be in different places based on the type of triangle. [/size][/size][/color]
The circumcenter of a triangle can be in different places based on the type of triangle. 

Check Your Understanding

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

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  • B
  • C
  • D
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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)?