Isosceles triangle given the base and one side

How to construct (draw) an isosceles triangle with compass and straightedge or ruler, given the length of the base and one side. First we copy the base segment. Then we use the fact that both sides of an isosceles triangle have the same length to mark the apex (topmost point) of the triangle the same distance from each end of the base.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.


The image below is the final drawing from the above animation.

  Argument Reason
1 PR = CD By construction. PR is a copy of the segment CD. See Copying a line segment for method and proof.
2 QP = QR = AB QP, QR both drawn with same compass width AB..
3 QPR is an isosceles triangle, with base CD and side AB. An isosceles triangle has two sides the same length..

  - Q.E.D

Try it yourself

Click here for a printable isosceles construction worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.

Other constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions