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Junior high school mathematics problem proof diamond
The quadrilateral BCEF is a diamond.

Proof: connect BE and AD at n point.

∫ Quadrilateral AEDB is a parallelogram,

∴AN=DN,BN=EN.

∫AF = DC = 2,

∴FN=CN=6/2=3,

The quadrilateral FECB is a parallelogram.

∫AC = 2+6 = 8, ∠ ABC = 90, AB=2 root number 10,

∴ CB = root sign [8? -(2 digits 10)? ] = the square root of 2 6.

∴ the root number of bn = 2/the square root of kloc-0/0× 2 6 ÷ 8 = the root number 15.

∵3? +(root number 15)? = = the square root of 2 6.

△ BNC is Rt△.

∴BE⊥FC.

The quadrilateral BCEF is a diamond.

Hope to adopt!