It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG

It is known that in square ABCD, e is a point on diagonal BD, passing through e, make ef ⊥ BD, intersect BC with F, connect DF, G is the midpoint of DF, connect eg, CG

It is proved that: ∵ EF ⊥ BD, ∵ DEF is a right triangle, ∵ G is the middle point of DF, ∵ eg = 12df, (the middle line on the hypotenuse of the right triangle is equal to half of the hypotenuse), in square ABCD, ∠ BCD = 90 °, G is the middle point of DF, ∵ CG = 12df, (the middle line on the hypotenuse of the right triangle is equal to half of the hypotenuse), ∵ eg = CG