Me

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.

Look at the picture.

∠GDF and ∠GBE are Alternate Interior Angles.

AB and CD are parallel therefore m∠GDF = m∠GBE.

∠EGB and ∠FGD are Vertical Angles, therefore m∠EGB = m∠FGD.

The point E and F are the midpoints of AB and CD. Therefore EB ≅ FD.

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent (AAS).

ΔEBG ≅ ΔFDG, therefore GE ≅ GF.

Conclusion: G is the midpoint of EF.

250

step-by-step explanation: