>How would I construct
>(A) an isosceles triangle if only given the altitude to the
>base and a base angle? This is the same as constracting a right triangle, given a side and an angle.
>
>(B) an isosceles trapezoid if only given the bases and the
>diagonal?
Drop perpendiculars from the endpoints of the smaller base.
>
>(C) a right triangle given the leg and the radius of the
>circumscribed circle?
An inscribed angle that subtends a diameter of a circle is right.