5.2. Perpendicular Bisectors http://www.ck12.org
Example B
←→
OQis the perpendicular bisector ofMP.
a) Which segments are equal?
b) Findx.
c) IsLon
←→
OQ? How do you know?Answer:
a)ML=LPbecause they are both 15.
MO=OPbecauseOis the midpoint ofMP
MQ=QPbecauseQis on the perpendicular bisector ofMP.
b)
4 x+ 3 = 11
4 x= 8
x= 2c) Yes,Lis on
←→
OQbecauseML=LP(Perpendicular Bisector Theorem Converse).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.