Triangle abc and angles acb in triangles A, B and C are known, as shown in the figure. .....

Solution: In a right triangle, the center line of the hypotenuse is equal to half of the hypotenuse, that is, CD = 1/2ab = ad, c'd' = 1/2a 'b' = a'd'

Because CD=C'D', AB = a' b' and AD = a' d'

In Rt△CED and Rt△C'E'D', CE = C 'e' and AD = A'd', so Rt△CED≌Rt△C'E'D'(HL).

So ∠CAD=∠C'A'D', CD = C'd' and AD = A'd', so △ CDA △ C'd 'a (SAS).

So AC=A'C', in Rt△ABC and Rt△A'B'C, AC = a' c, AB = a' b'

So Rt△ABC≌Rt△A'B'C'(HL)

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