Triangle Proportionality and Triangle Angle-Bisector Theorems
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Students learn the following theorems related to similar triangles. If a line is parallel to a side of a triangle, and it intersects the other two sides of the triangle, then it divides these sides proportionally (Triangle Proportionality Theorem). If three parallel lines intersect two transversals, then they divide the transversals proportionally (Corollary of the Triangle Proportionality Theorem). If a ray bisects an angle of a triangle, then it divides the opposite side of the triangle into segments that are proportional to the other two sides (Triangle Angle-Bisector Theorem). Students are then asked to solve problems related to these theorems using Algebra.