SOLUTION: In parallelogram ABCD, E is the midpoint of AB and F is the midpoint of DC . Let G be the intersection of the diagonal DB and the line segment EF . Prove that G is the

Algebra ->  Geometry-proofs -> SOLUTION: In parallelogram ABCD, E is the midpoint of AB and F is the midpoint of DC . Let G be the intersection of the diagonal DB and the line segment EF . Prove that G is the       Log On


   

Question 1136360: In parallelogram ABCD, E is the midpoint of
AB
and F is the midpoint of
DC
. Let G be the intersection of the diagonal
DB
and the line segment
EF
. Prove that G is the midpoint of
EF.
△EGB = △
by reason
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


AE, BE, CF, and DF are all congruent because they are each half of sides AB and CD, which are congruent because they are opposite sides of a parallelogram.

In triangles EGB and FGD, all three corresponding pairs of angles are congruent.

Then with sides BE and DF congruent, triangles EGB and FGD are congruent, making EG congruent to GF; and that makes G the midpoint of EF.