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... vertical angles, and the theorem for interior angles on the same side of the transversal follows by  applying linear pairs.  Alternatively, we can prove alternate interior angles are congruent by a transformational argument.   Locate the midpoint on the transversal between the two points of intersec ...
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... A1. Problems A, B and C were posed in a mathematical contest. 25 competitors solved at least one of the three. Amongst those who did not solve A, twice as many solved B as C. The number solving only A was one more than the number solving A and at least one other. The number solving just A equalled t ...
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