It is known that: as shown in the figure, in RT △ ABC, ∠ C = 90 ° and ∠ a = 30 ° take AB and AC as edges respectively, and make equilateral △ Abe and equilateral △ ACD on the outside of △ ABC, de and ab intersect with F, proving: EF = FD

It is known that: as shown in the figure, in RT △ ABC, ∠ C = 90 ° and ∠ a = 30 ° take AB and AC as edges respectively, and make equilateral △ Abe and equilateral △ ACD on the outside of △ ABC, de and ab intersect with F, proving: EF = FD

It is proved that if eg and ab are made by e over g, as shown in the figure, ∵ Abe is an equilateral triangle, ∵ BG = 12ab, ∵ Abe = ∵ bea = ∵ EAB = 60 ° AE = AB, ∵ RT △ ABC, ∵ C = 90 °, ∵ a = 30 ° BC = 12ab, ∵ Ag = BC, in RT △ EAG and RT △ ABC, AE = abag = BC, ≌ RT △ EAG ≌ RT △ ABC (HL