Title:

The quadrilateral ABCD is a parallelogram with AD=2AB and point E is the midpoint of AD. Explain the positional relationship BEtween be and EC.

Solution: BE⊥CE. The reasons are as follows:

AD = 2AE = 2DE，？ AD=2AB？ ∴AE=DE=AB

∴∠aeb=∠abe= 1/2( 180-∠a)= 90- 1/2∠a

Parallelogram in AB=CD∴DE=CD.

∴∠DEC=∠DCE=90 ﹣ 1/2∠D

∴∠aeb+∠dec= 180- 1/2(∠a+∠d)

∵∠A+∠D= 180

∴∠AEB+∠DEC=90

∴∠BEC= 180 ﹣(∠AEB+∠DEC)=90

∴BE⊥CE

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