November 11, 2013

# Perpendicular Bisectors of Triangles

###### What is a perpendicular bisector?

A perpendicular bisector of a line segment is a line that makes a 90-degree angle (a right angle) at the midpoint of a segment.

In the figure, line *b* is the perpendicular bisector of line segment AB at C. This implies AC=CB and the measure of the angles at C is 90 degrees.

Now, try the problem below.

###### Problem

In the figure below, the perpendicular bisectors of the sides of the three colored triangles are shown. They seem to intersect at a common point? Do they? Try connecting ** any three** of the pointsÂ B, C, D, E, F, G and then construct the perpendicular bisector of each the sides.

What may be true about the points B, C, D, E, F, G? Why?

Hint? Read the post below:

###### Theorems on Centroid, Orthocenter, and Circumcenter

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