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Isosceles Triangle given the leg length and apex angle
Geometry construction using a compass and straightedge

This construction produces an isosceles triangle given the length of the legs and the apex angle (the one at the top). The construction proceeds in two main steps:

  1. Copy the angle, making sure each leg of the angle is longer than the desired side length of the triangle. This is exactly the same as the construction Copying an angle with compass and straightedge.
  2. Mark off the length of the two legs of the triangle and draw the base line.

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.

Proof

  Argument Reason
1 Angles BAC and QPR are congruent By construction. See Copying an angle with compass and straightedge.
2 Line segments FG, PQ and PR are congruent All drawn with the same compass width.
3 PQR is an isosceles triangle with the given apex angle and leg length. An isosceles triangle is a triangle with two congruent legs. See Isosceles triangle definition.

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing two triangle construction problems. 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

Lines

Angles

Triangles

Right triangles

Triangle Centers

Circles, Arcs and Ellipses

Polygons

Non-Euclidean constructions