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In parallelogram ABCD, point E is the midpoint of side BC, connecting de and extending the extension line of intersection AB to point F, then CD=BF? Try to explain why.

Eight-character congruence, first prove three △ BFE △ ECD, and you can find CD=BF.

Solution: CD=BF for the following reasons:

Point e is the midpoint of BC.

∴BE=BC

∵ABCD is a parallelogram.

∴AB//CD

∴∠FBE=∠ECD

In △BEF and △CED.

∠BEF=∠CED

BE=BC

∠FBE=∠ECD

∴△BEF≌△CED

∴CD=BF