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Revise earlier work on the necessary and sufficient conditions for polygons to be similar.
Prove (accepting results established in earlier grades): * that a line drawn parallel to one side of a triangle divides the other two sides proportionally (and the Mid-point Theorem as a special case of this theorem); * that equiangular triangles are similar; * that triangles with sides in proportion are similar; and * the Pythagorean Theorem by similar triangles.