Geometry Constructions

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A series of free, online High School Geometry Video Lessons and solutions.
Examples, solutions, videos, worksheets, and activities to help Geometry students.

In these lessons, we will learn

• how to construct and duplicate a line segment
• how to construct and duplicate an angle
• how to construct a perpendicular bisector
• how to construct a perpendicular line through a point on the line
• how to construct a perpendicular line through a point not on the line.

Duplicating a Line Segment

When constructing a line segment, we use a compass and straightedge to first draw a ray or line and then a point that will serve as an endpoint of the new segment. Next, we measure the given segment with a compass and make a mark with the pencil end. Without changing the spacing of the compass, place the sharp end of the compass on the point drawn on the new line/ray, and make a mark on the line/ray.

How to duplicate a line segment using a compass and straightedge?

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How to use a compass and straightedge to construct a congruent segment?

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Duplicating an Angle

When constructing an angle, first swing an arc from the vertex of your angle. Then, swing a congruent arc from the new vertex. Return to the original angle; the drawn arc intersected the sides of the angle - measure this distance. On the new angle, place the sharp end of the compass on the intersection of the arc and ray and draw another arc. Draw a ray connecting the new vertex with the point of intersection.

How to duplicate an angle using a compass and straightedge?

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How to use a compass and straightedge to construct a congruent angle?

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Constructing the Perpendicular Bisector

When looking at a line segment, there is only one line that will pass through the midpoint that will be a constant distance between the two endpoints. This line is called the perpendicular bisector. To construct the perpendicular bisector, we first find the midpoint of the line segment and then use a compass and straightedge to draw the perpendicular line.

How to define a perpendicular bisector?

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How to use a straight edge and a compass to bisect a segment?

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Constructing a Perpendicular at a Point on a Line

When constructing a perpendicular bisector, we are specifically being asked to construct a line perpendicular to a line through the midpoint. To construct a perpendicular to a line through a point like the midpoint, we use a process similar to constructing a perpendicular to a line through a point not on the line. To construct a perpendicular, we use a compass and straightedge to determine a point equidistant from two equidistant points on the line.
Perpendicular Line(1) Construction
How to use a compass and straightedge to construct a perpendicular line through a point on the line?

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Constructing a Perpendicular to a Line

The shortest distance between a point not on a line and a line is along the perpendicular to the line. Constructing a perpendicular to a line uses the same process as constructing the perpendicular bisector of a line segment, but with one additional step. The first step is to swing an arc from the point and intersect the line in two places, which creates a segment that can be bisected.

Perpendicular Line(2) Construction
How to use a compass and straightedge to construct a perpendicular line through a point not on the line?

• Show Step-by-step Solutions

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