Geometry problem,very intersting, please check!! 1. The problem statement, all variables and given/known data In the figure,AH=HC and AB=DC,measure of angle A is 54.Whats the measure of the angle C? [PLAIN]http://img685.imageshack.us/img685/9144/gty.png [Broken] 2. Relevant equations Isosceles triangle theorem, altitudes ,medians ,angle bisectors... 3. The attempt at a solution I have tried to extend a line segment A to D which is equal to the line segment DC. Now we have an Isosceles triangle DAC.Since we now that in an isosceles triangle the altitude which is drawn from the vertex of the triangle is also median and angle bisector.So the angle D or the vertex is bisected in to two congruent angles. And if to sides are equal DA with DC and also the angles opposite them should be equal. We can name the angles which are congruent as ones that are congruent with the letter a and the others with letter b.The sum of these will be a+b=90. And then I don't know what to do???