Using only a compass and straightedge, construct a square given one of its sides a.

Question

___________________
a

Answer 1

Use the idea that any segment from the base of the triangle to a line parallel to the base and through vertex A will be an altitude of ?ABC as well as ?ABM1 , ?ABM2 and ?ACM3.With the same altitude it is sufficient to use Construction 8 to form points M1 and M2.