Question

PLEASE HELP 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.

Answer 1

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.