1. Objective: Students will use proportional parts of triangles and divide a segment into parts. S. Calahan 2008

2. Triangle Proportionality Theorem If a line is parallel to one side of a triangle and intersects the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. C D E A B If BD || AE, BA ≈ DE CB CD

3. Find the length of a side In ABC, BD || AE, AB = 9, BC = 21, and DE = 6. Find DC. C D E A B

4. Find the length of a side From the Triangle Proportionality Theorem BA ≈ DE CB CD Substitute the know measures. C D E A B

5. Find the length of a side 9 = 6 Let x = DC 21 x 9(x) =21(6) 9x = 126 x = 14 Therefore, DC = 14 C D E A B

6. Triangle Midsegment Theorem C D E A B A midsegment of a triangle is parallel to one side of the triangle, and its length is ½ the length of that side. If B and D are midpoints of AC and EC respectively, BD || AE and BD = ½ AE.

7. Midsegment of a Triangle If AE = 12 then BD = ½(12) = 6. C D E A B

8. Divide Segments Proportionally If three or more parallel lines intersect two transversals, then they cut off the transversal proportionally. D E F A B C AB = DE, AC = BC, and AC = DF BC EF DF EF BC EF