[size=150]The center of a [b]triangle's[/b] circumcircle. It is where the "perpendicular bisectors" (lines that are at right angles to the midpoint of each side) meet.[/size]
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[br]2) Using the COMPASS TOOL, create a circle with radius AB and center point B[br]3) Using the SEGMENT TOOL, draw a segment that connects the intersections of circles A and B[br]4) Using the POINT TOOL, mark point E at the intersection of segments AB and CD[br][br][i]RESULTS: Segment CD is the [b]Perpendicular Bisector [/b]of segment AB[br] Point E is the [b]Midpoint[/b] of segment AB[/i]
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[br]2) Using the COMPASS TOOL, create a circle with radius AD and center point A[br]3) Using the POINT TOOL, mark point F where circle A intersects segment AC[br]4) Using the COMPASS TOOL, create a circle with the radius DF and center point D[br]5) Using the COMPASS TOOL, create a circle with the radius DF and center point F[br]6) Using the SEGMENT TOOL, draw a segment from point A to the intersection of circles D and F[br][br][i]RESULTS: Segment AG is the Angle Bisector of angle CAB[/i]
Check Your Understanding
What does the term angle bisector mean?
The Circumcenter of a Triangle
[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]
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)?