1. As shown in the figure, △ABC is an equilateral triangle, D and F are points on BC and AB respectively, CD=BF, and AD is an edge △ADE. When d is on the BC line, the quadrilateral CDEF is a parallelogram, and ∠ DEF = 30? Prove your conclusion.

Solution:?

When b is at the midpoint of BC, the quadrilateral CDEF is a parallelogram, ∠ def = 30; In △ADC and △BFC, BF = DC, BC = AC, ∠ B = ∠ ACD ∴△ ADC △ ≌ BFC ∴ AD = FC, ∠DAC =∠BCF = 30∠aed are Bad = 60 ∴ AD bisects the vertical ED ∴ BDE = ∠ DCF = 30 ∴ ED ∴ FC ∴ CDEF is a parallelogram and ∠ DEF = 30.