As shown in the figure, ∠ ABC = 30 ° in △ ABC, take BC and AC as sides, make equilateral △ BCD and equilateral △ ace, connect be, and prove AB square + BC square = be square Such as the title

1. Connect ad
2. ∠ bad = 30 ° + 60 ° = 90 ° so ab ⊥ BD
3. △ ACD ≌ △ CEB (AC = CE, BC = DC, ∠ BCE = ∠ DCA, i.e. s, a, s)
So ad = be, BC = BD, △ abd is a right triangle, AB ^ 2 + BD ^ 2 = ad ^ 2. That is ab ^ 2 + BC ^ 2 = be ^ 2

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