The Triangle Proportionality Theorems — Angle Bisectors of a Triangle and Proportional Parts

About this lesson

This unit teaches the properties of angle bisectors in triangles. It covers the interior and exterior angle bisectors of a triangle, explaining that the bisector of an interior or exterior angle at a vertex divides the opposite side internally or externally into segments whose lengths are proportional to the lengths of the other two sides. The unit includes proofs (though not required for the main theorem), worked examples, and exercises for calculating lengths of segments and bisectors, and for proving lines parallel using these properties. It also introduces the formula for the length of an interior angle bisector and an exterior angle bisector, and notes that the bisectors of the angles of a triangle are concurrent. Students are expected to apply these theorems to solve problems, including life problems, and to use proportions to find unknown lengths.