This demonstration shows how to draw an isosceles triangle, using only a compass and straight edge, given the base and altitude (height). See "Introduction to Euclidean Constructions".

We start with two line segments AB and CD that define the desired length of the base and the altitude of the triangle. The result is an isosceles triangle PQR. For more information, see Definition and Properties of an Isosceles Triangle.

Step 1	Draw a point P that will become one end of the base of the triangle.
Step 2	Place the point of the compass on the point C and adjust the compass width to the desired length CD of the base of the finished triangle
Step 3	With the compass point on P, make an arc near the other end of the base of the triangle.
Step 4	Pick a point R anywhere on the arc. This will become the other end of the base of the triangle.
Step 5	Draw the base line PR.
Step 6	With the compass width set roughly to the base length (exact width is not important), draw an arc above and below the base line from points P and R.
Step 7	Draw a line through the two arc intersections. This is the perpendicular bisector of the base, dividing it into two equal parts.
Step 8	Set the compass width to the distance from A to B. This is the desired altitude of the triangle.
Step 9	Place the point of the compass on the midpoint of the base line, and draw an arc across the perpendicular drawn earlier. This is the third vertex of the triangle.
Step 10	Draw the two side lines PQ and RQ
Step 11	Done. The triangle PQR is an isosceles triangle.