Prove that efgh is a parallelogram In the parallelogram ABCD, e, F, G and H are points on AB, BC, CD and ad respectively, and AE = CG, BF = DH, Verification: the quadrilateral efgh is a parallelogram And it should be explained in words.

Prove that efgh is a parallelogram In the parallelogram ABCD, e, F, G and H are points on AB, BC, CD and ad respectively, and AE = CG, BF = DH, Verification: the quadrilateral efgh is a parallelogram And it should be explained in words.

It is proved that ab = CD, ad = BC because ABCD is a parallelogram; angle a = angle c, angle B = angle D, AE = CG, BF = DH can be obtained from known; EB = ab-ae, Gd = cd-cg, so EB = Gd, because EB = Gd, BF = HD, angle B = angle D, so △ EBF ≌ △ HDG, so EF = Hg, eh = FG, because two opposite sides are equal respectively

As shown in the figure, it is known that the quadrilateral ABCD is a parallelogram. On the extension line of AB, intercept be = AB, BF = BD, connect CE and DF, and intersect at point M. verification: CD = cm

It is proved that: ∵ quadrilateral ABCD is a parallelogram, ∵ AB is parallel and equal to DC. And ∵ be = AB, ∵ be is parallel and equal to DC. The ∵ quadrilateral bdce is a parallelogram. ∵ DC ∵ BF, ∵ CDF = ∵ F. similarly, ∵ BDM = ∵ DMC. ∵ BD = BF, ∵ BDF = ∵ f.