Question

in adjoining figure abcd is parallelogram in which e and f are the mid point of an and CD respectively if gh is a line segment that cuts and, ef, and bc at g, p, and h respectively prove that gp equal to ph

Answer 1

Draw a line through P which is parallel to AB and CD. Let this new line intersect AD and BC at points X and Y respectively.  

Now prove that triangles PGX and PYH are congruent via AAS.  

Use the equality of alternate interior angles, vertically opposite angles and sides of a parallelogram to prove the congruence.

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