7 4 Notes Parallel Lines and Proportional Parts

7. 4 Notes Parallel Lines and Proportional Parts Today’s Objectives: 1. Students will be able to use proportional parts within triangles. 2. Students will be able to use proportional parts with parallel lines.

- If a line is parallel to one side of a triangle and intersects the other two sides, then it divides the sides into segments of proportional lengths. Triangle Proportionality Theorem

Example 1 a) In Find SU. , SV = 3, VR = 8, and UT = 12.

Example 1 cont. b) In Find BY. , AX = 4, XB = 10. 5, and CY = 6.

You Try! •

Converse of Triangle Proportionality Theorem If a line intersects two sides of a triangle and separates the sides into proportional corresponding segments, then the line is parallel to the 3 rd side of the triangle.

Example 2 a) whether . Explain. Determine

Example 2 cont. •

Midsegment of a Triangle - A segment with endpoints that are midpoints of two sides of the triangle. - A midsegment of a triangle is parallel to Midsegment one side of the triangle, and its length is one Theorem half the length of that side.

Example 3 •

Example 3 cont. •

- If 3 or more parallel lines intersect two transversals, then they cut off the transversals proportionally. Proportional Parts of Parallel Lines

Example 4 In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in between city blocks. Find the value of x.

- If 3 or more parallel lines cut off congruent segments on one transversal, Congruent then they cut off congruent segments on Parts of every transversal. Parallel Lines

Example 5 Find the values of x and y.

Summary

Summary

Summary

Homework: pg. 495, #10 – 24 even, 38, 40