# Constructing an isosceles triangle given base and altitude

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We start with two line segments AB and CD that define the altitude and the base length 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, draw 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.
In the next three steps, we form the perpendicular bisctor of the base
6.  With the compasses' width set roughly to the base length (exact width is not important), draw an arc on each side of the base line from points P and R.
7.  Draw a line through the two arc intersections. This is the perpendicular bisector of the base, dividing it into two equal parts.
8.  Set the compasses' width to the distance from A to B. This is the desired altitude of the triangle.
9.  Place the point of the compasses on the midpoint of the base line, and draw an arc across the perpendicular drawn earlier. This is the third vertex of the triangle.
10.  Draw the two side lines PQ and RQ
11.  Done. The triangle PQR is an isosceles triangle.