http://www.ck12.org Chapter 5. Relationships with Triangles
Example C
For further exploration, try the following:
- Cut out an acute triangle from a sheet of paper.
- Fold the triangle over one side so that the side is folded in half. Crease.
- Repeat for the other two sides. What do you notice?
The folds (blue dashed lines)are the perpendicular bisectors and cross at the circumcenter.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter5PerpendicularBisectorsB
Concept Problem Revisited
The center of the circle will be the circumcenter of the triangle formed by the three bones. Construct the perpen-
dicular bisector of at least two sides to find the circumcenter. After locating the circumcenter, the archeologist can
measure the distance from each bone to it, which would be the radius of the circle. This length is approximately 4.7
meters.
Vocabulary
Perpendicular linesare lines that meet at right (90◦) angles. Amidpointis the point on a segment that divides the
segment into two equal parts. Aperpendicular bisectoris a line that intersects a line segment at its midpoint and is
perpendicular to that line segment. When we construct perpendicular bisectors for the sides of a triangle, they meet
in one point. This point is called thecircumcenterof the triangle.
Guided Practice
- Find the value ofx.mis the perpendicular bisector ofAB.
- Determine if
←→
STis the perpendicular bisector ofXY. Explain why or why not.Answers:
- By the Perpendicular Bisector Theorem, both segments are equal. Set up and solve an equation.
x+ 6 = 22
x= 162.
←→
STis not necessarily the perpendicular bisector ofXYbecause not enough information is given in the diagram.
There is no way to know from the diagram if
←→
STwill extend to make a right angle withXY.