Section 7-5 Proportions in Triangles

1. Section 7-5 Proportions in Triangles • Objectives: • Use Side-splitter Theorem and the Triangle-Angle-Bisector Theorem Similar triangles can be used to solve a variety of problems.

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

3. Apply the Side-Splitter Theorem Find the length of VX by using the side splitter theorem.

4. Corollary to Side-Splitter Theorem Theorem 8-4 Corollary to Side-Splitter Theorem If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

5. Apply the Corollary to the Side-Splitter Theorem Find the value of x from the diagram below.

6. Real-world Connection Sail makers sometimes use a computer to create patterns for sails. After the panels are cut out, they are sown together to form the sail. The edges of the panels in the sail to the right are parallel. Find the lengths of x and y.

7. Triangle-Angle Bisector Theorem Theorem 8-5 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. CA • DB = CD • BA

8. Using the Triangle-Angle Bisector Theorem Find the unknown value for the given information.