China Naming Network - Almanac query - 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.
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