Constructions

Geometric Constructions ... Animated!

"Construction" in Geometry means to draw shapes, angles or lines accurately.

These constructions use only compass, straightedge (i.e. ruler) and a pencil.

This is the "pure" form of geometric construction: no numbers involved!

Basics

Learn these two first, they are used a lot:

Line Segment Bisector and Right Angle

Angle Bisector

Points and Lines

Copy a Line Segment

Add Line Segments

Subtract Line Segments

Perpendicular to a Point on a Line

Perpendicular to a Point NOT on a Line

Perpendicular to Start of a Ray

Parallel Line through a Point (by Angles)

Parallel Line through a Point (by Rhombus)

Parallel Line through a Point (by Triangles)

Cut a line into n equal segments

Angles

And it is useful to know how to do 30°, 45° and 60° angles. We can use the angle bisector method (above) to create other angles such as 15°, etc.

Same (Congruent) Angle

30° Degree Angle

45° Degree Angle

60° Degree Angle

90° Degree Angle

Add Angles

Subtract Angles

Triangle Basics

Copy a triangle

Equilateral Triangle

Triangle Altitudes

Triangle Midsegment

Triangle Centers

Inscribe a Circle in a Triangle

Circumscribe a Circle on a Triangle

Circle Basics

Circle Center and Diameter

Circle Center by Two Chords

Circle Center by Right Angles

Circle Touching 3 Points

Circles and Tangents

Tangents to Point Outside Circle

Tangent to Point on Circle

Polygons

And for the "Master Class":

Square from One Side

Square Inscribed in a Circle

Pentagon

Hexagon from One Side

(Note: You can also see how to Use the Protractor, Use the Drafting Triangle and Ruler, and How to construct a Triangle With 3 Known Sides, but they are not "pure" geometric constructions.)