Straightedge and Compass

We can use a straightedge and compass to construct geometric figures, such as angles, triangles, regular n-gon, and others. In this case, measuring instruments such as a ruler and a protractor are not permitted. 

Straightedge and compass

A ruler can be used if and only if its markings are not used. Below, find a variety of important constructions in geometry.

Using a straightedge and compass to construct angles, triangles, quadrilaterals, perpendicular, and others.

Bisecting and copying angles

Bisecting an angle
Learn how to bisect a given angle. Nice and fully illustrated demonstration.

Copying an angle
Learn how to copy any angle. In other words, you will construct an angle congruent to a given angle. Learn to do this with ease using step by step guidelines.

Constructing perpendiculars and midpoint of a segment

Constructing perpendiculars
Learn how construct a line perpendicular to another line through a point on the line or not on line.

Constructing the midpoint of a segment
Learn how to use only a ruler and a compass to get the midpoint of a segment.

Constructing triangles

Constructing an equilateral triangle
Learn how construct an equilateral triangle given the length of any segment. 

Constructing an isosceles triangle
Learn how construct an isosceles triangle given the lengths of two congruent segments.  

Constructing quadrilaterals

How to construct a square
Learn how to construct a square using a straightedge and a compass.

Other constructions that can be done using only a straightedge and compass.

  • You can construct a scalene triangle when the length of the three sides are given.
  • You can construct a right triangle given the length of its hypotenuse and the length of a leg.
  • You can construct a triangle when the length of two sides are given and the angle between the two sides. 
  • You can construct a line segment that is congruent to a given line segment.
  • You can construct a triangle when two angles and the included side are given.
  • You can construct a line parallel to a given line through a point that is not located on the given line.
  • You can construct a tangent to a given circle through a given point that is located on the given circle.
  • You can construct a tangent to a given circle through a given point that is not located on the given circle.
  • You can construct a regular pentagon.
  • You can construct a regular hexagon.
  • You can construct a regular octagon.
  • You can construct a regular decagon.

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