As shown in the figure, in the triangle ABC, the angle c = 90 degrees, AC = BC, ad bisector angle BAC, intersection BC at point D, de vertical AB, perpendicular foot E. try to explain the reason why AB = AC + CD

It is proved that the triangle ACD is equal to the triangle AED, so AC = AE, CD = de. the triangle DEB is isosceles right triangle, so de = be, so AB = AE + EB = AC + de = AC + DC

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