SOLUTION: Given: Quadrilateral ABCD is a parallelogram.Segment DE is perpendicular to Segment AC, Segment GF is perpendicular to Segment AC. Prove: AE plus CF all over CF is equal to ED plu

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Question 806126: Given: Quadrilateral ABCD is a parallelogram.Segment DE is perpendicular to Segment AC, Segment GF is perpendicular to Segment AC.
Prove: AE plus CF all over CF is equal to ED plus FG all over FG
Please!!! TOTALLY NEED THE ANSWER!!!!
Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
DE is perpendicular to AC
GF is perpendicular to AX
so DE is parallel to GF
In triangle DEC & GFC
angle DEC is congruent to triangle GFC
Angle EDC is congruent to FGC ( corresponding angles)
so the triangles are similar by AA test of similarity
Therefore EC/FC = ED/FG = DC/GC ratios of corresponding sides are equal
But EC = AC ( diagonals of a parallelogram bisect each other)

Therefore (AC+FC)/FC = (ED+FG)/FG ( by componendo)