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Geometric Constructions

Videos and lessons with examples and solutions to help High School students learn how to make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).


Lessons here include:

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.

Common Core: HSG-CO.D.12

Basic Geometric Constructions - copying line segments, angles and triangles
How to copy line segments, angles and triangles using a compass and a straight edge.

Bisecting an Angle
How to bisect an angle using a compass and a straight edge.

Constructing a Perpendicular Bisector of a Line Segment
How to construct a perpendicular line bisector using a compass and a straight edge.

Constructing a Line Parallel to a Given Point
How to construct a parallel line through a given point by using a straight edge and a compass.

Bisecting an Angle Efficiently
It is well-known that an angle can be bisected in the traditional way by drawing three arcs. However, it is possible to bisect an angle by drawing two arcs and two lines instead. This Demonstration shows one such method. Two concentric circles are constructed, centered on the angle to be bisected. The intersection of the two lines shown produces the desired bisection.

Bisection of Line Segment
Bisect a line segment with compass and straight edge.

Patty Paper - Angle Bisectors
How to fold an angle bisector in a triangle using Patty Paper.

Patty Paper - Perpendicular Bisector
How to fold a midpoint or a perpendicular bisector using Patty Paper

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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