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.

perpendicular bisector

Now, try the problem below.


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 points 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?

inscribing triangles

Hint? Read the post below:

Theorems on Centroid, Orthocenter, and Circumcenter
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