
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 stepbystep instructions
The above animation is available as a
printable stepbystep instruction sheet, which can be used for making handouts
or when a computer is not available.
Proof
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
Lines
Angles
Triangles
Right triangles
Triangle Centers
Circles, Arcs and Ellipses
Polygons
NonEuclidean constructions
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