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Bisecting an Angle
Geometry & Algebra II Archive
Geo U1: Tools of Geometry
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Bisecting an Angle

Geometry & Algebra II Archive

Geo U1: Tools of Geometry

Big Idea: Big Idea 2

<style type="text/css"><!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> </style> 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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Type
Geometry: Tools of Geometry
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External Link
Tags
angle bisector, bisector
Standards
Common Core: Supporting Standards ( G-CO.A.1, G-CO.A.2, G-CO.D.12 )
+— Details
Common Core: Supporting Standards:
G-CO.A.1

Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.A.2

Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.D.12

Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

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Perpendicular Bisector
Resource:
Perpendicular Bisector

Geometry & Algebra II Archive

Geo U1: Tools of Geometry

Big Idea: Big Idea 1

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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Type
Geometry: Tools of Geometry
File
Google Doc
Tags
bisector
Standards
Common Core: Supporting Standards ( G-CO.A.1, G-CO.A.2, G-CO.D.12 )
+— Details
Common Core: Supporting Standards:
G-CO.A.1

Experiment with transformations in the plane. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.A.2

Experiment with transformations in the plane. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.D.12

Make geometric constructions. Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Clarification: Constructions include but are not limited to the listed constructions. Example: constructing the median of a triangle or constructing an isosceles triangle with given lengths.

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