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Angle Bisector and Perpendicular at a Point

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Angle Bisector and Perpendicular at a Point

The last construction lesson in the series is for the Angle Bisector.  I struggled with the scaffold to get students to make the first arc on the page.  After they made the arc, the rest of the page was achievable by all.  I was especially impressed with how easy it was to transition from the first construction to the second for students.

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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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