Geometric Constructions
Related Topics:
More Geometry Lessons
In these lessons, we will learn how to use a pair of compasses and a straight-edge to construct different geometric shapes given certain conditions.
Geometric constructions involve drawing geometric shapes that satisfy certain requirements using a straight-edge and a pair of compasses.
The tools to use are a ruler (or straight-edge) and a pair of compasses.
A few points to remember when doing the types of geometric constructions covered in these lessons:
- Do not use a protractor
- Use a sharp pencil
- Do not erase the construction lines. (They will show the examiner how the lines or shapes were constructed)
The following diagram shows some examples of constructions: Perpendicular Bisector, Perpendicular Line through a Point, Angle Bisector. Scroll down the page for more examples and solutions.
Geometry Worksheets
Practice your Geometry skills with the following worksheets:
Printable & Online Geometry Worksheets
Common Geometric Constructions:
Here are some of the frequently used geometric constructions:
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Copying a Line Segment: Given a line segment, construct another line segment of the same length.
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Constructing a Perpendicular Bisector: Given a line segment, construct a line that is perpendicular to it and passes through its midpoint.
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Constructing an Angle Bisector: Given an angle, construct a ray that divides the angle into two equal angles.
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Constructing a Perpendicular to a Line (from a point on the line or from a point not on the line): Drawing a line that forms a 90-degree angle with a given line.
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Constructing a Parallel Line: Given a line and a point not on the line, construct a line parallel to the given line that passes through the point.
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Constructing a Triangle (SSS): Construct A Triangle Given The Length Of Its Three Sides.
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Constructing a Triangle (SAS): Construct A Triangle Given Two Sides And An Included Angle.
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Constructing a Triangle (AAS): Construct A Triangle Given One Side And Two Angles.
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Constructing an Equilateral Triangle: Construct a triangle with all three sides of equal length. Each angle will be 60°.
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Constructing a 30° Angle: Construct a 30° angle by bisecting a 60° angle.
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Constructing a 45° Angle: Construct a 45° angle by bisecting a 90° angle.
This video shows how to copy a line segment using a compass and straight-edge.
This video shows how to copy an angle using a compass and straight-edge.
This video shows how to construct perpendicular bisectors.
This video shows how to use a compass and straightedge to construct a perpendicular to a given line through a point not on that line.
This video shows how to use a compass and straightedge to construct an angle bisector.
This video shows how to a compass and straightedge to construct a line parallel to a given line through a given point not on that line using corresponding angles.
This video shows how to construct parallel lines using congruent alternate interior angles given the following information: a given line and a point not on that given line.
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