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Bisecting an Angle

Geometry
Unit 1: Tools of Geometry
Resource:
Bisecting an Angle

This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees. Since the rays forming a 180 degree angle are collinear, this case can be handled separately by constructing the perpendicular to a line through a given point: note that the construction in the collinear case is actually the same as the one employed here except that the two circles in step (b) need to have radii larger than r so that they meet in two points.
 

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Perpendicular Bisector

Resource:
Perpendicular Bisector

This is my second lesson in the series.  For this lesson, I had students create a perpendicular bisector. First, they went through the following steps off worksheet (1. Draw a segment, 2. Fold it in such a way that it is bisected, 3. Mark 3 points on the fold, and 4. Measure from each of the 3 points to the each endpoint.)  While all steps but 2 were mechanical in nature and did require a docucam or another way to show the process, the rest of the sheet was a hit and students made genuine connections on how the same radius is instrumental in creating a perpendicular bisector.

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