OBJECTIVES: 1) TO USE THE SIDE-SPLITTER THEOREM 2) TO USE THE TRIANGLE- ANGLE BISECTOR THEOREM 8-5 Proportions in Triangles M11.C.1

Side-Splitter Theorem 8-4 If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Example Use the side-splitter theorem to solve for x.

Example Find y.

Corollary If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

Example: Use Corollary The segments joining the sides of trapezoid RSTU are parallel to its bases. Find x and y

Example Solve for x and y.

Triangle-Angle-Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Example: Use the triangle-angle bisector Use the triangle-angle bisector theorem to find x.

Example Use the triangle-angle-bisector theorem to find y.