# Constructing an isosceles triangle given the base and one side

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We start with two line segments AB and CD that define the lengths of the legs and the base of the triangle.

1.  Draw a point P that will become one end of the base of the triangle.
2.  Place the point of the compasses on the point C and adjust the compasses' width to the desired length CD of the base of the finished triangle
3.  With the compasses' point on P, make an arc.
4.  Pick a point R anywhere on the arc. This will become the other end of the base of the triangle.
5.  Draw the base line PR.
6.  With the compasses' point on B, set its width to the desired side length - AB
7.  Without changing the compasses, make two intersecting arcs - one from P, the other from R to define the third vertex, Q, of the triangle.
8.  Draw the two side lines PQ and RQ
9.  Done. The triangle PQR is an isosceles triangle.