How to draw an isosceles triangle given the base and altitude with compass and straightedge or ruler. The base is the unequal side of the triangle and the altitude is the perpendicular height from the base to the apex. It works by first copying the base segment, then constructing its perpendicular bisector. The apex is then marked up from the base.
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.
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  QS is the perpendicular bisector of PR  By construction. See Constructing the perpendicular bisector of a line segment.. 
3  Triangles QPS and QRS are congruent.  SAS. See Test for congruence sideangleside.

4  QP = QR  CPCTC  Corresponding Parts of Congruent Triangles are Congruent 
5  QS = AB  By construction. 
6  QPR is an isosceles triangle.  From (4). An isosceles triangle has two sides the same length. 
7  QPR is an isosceles triangle with base CD and altitude AB.  From (1) (5) (6) 