1. PARALLEL LINES AND PROPORTIONAL PARTS
Use proportional parts of triangles
Divide a segment into parts

5. C B D A E

6. TRIANGLE PROPORTIONALITY THEOREM
If a line is parallel to one side of a triangle and intersects the other two sides at two distinct points, then it separates these sides into segments of proportional lengths. C
Example: B D A E

7. Example 1 – Find the Length of a Side
Find x
From the Triangle Proportionality Theorem, E F
Substitute the known measures: 9 6 H L 21 x
Cross products
Multiply
Divide each side by 9 G

8. TRIANGLE PROPORTIONALITY THEOREM
CONVERSE OF THE
TRIANGLE PROPORTIONALITY THEOREM
If a line intersects two sides of a triangle and separates the sides into corresponding segments of proportional lengths, then the line is parallel to the third side. C
Example: D B E A

9. DEFINITION
A Midsegment of a triangle is a segment whose endpoints are the midpoints of two sides of the triangle. C
A Midsegment D B E A

10. TRIANGLE MIDSEGMENT THEOREM
A midsegment of a triangle is parallel to one side of the triangle and its length is one half the length of that side. C D B E A

11. Example 2 – Find x and y

12. Example 3 – Find x