The convex quadrilateral ABCD satisfies the following relations: ∠DAB = ∠ABC = 60 and ∠CAB = ∠CBD. Prove that AD + CB = AB
Let us extend the sides AD and BC until they intersect at some point E, then the triangle ABE is equilateral.
Let us prove that BC = ED. In triangles ABC and BED: AB = BE; ∠CAB = ∠DBE, ∠ABC = 60 ° = ∠BED. Thus, these triangles are equal in the second attribute. Therefore, BC = ED.
Thus, AD + CB = AD + ED = AE = AB.
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