1. NOTEBOOK CHECK TOMORROW!

2. Proportions and Similar Triangles
Section 8.6:
Proportions and Similar Triangles

3. Theorem 8.4: Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. If TU ║ QS, then

4. Theorem 8.5: Converse of the Proportionality Theorem
If a line divides two sides of a triangle proportionally, then it is parallel to the third side. If
, then TU ║ QS.

5. Theorem 8.6 If three parallel lines intersect two transversals,
then they divide the transversals proportionally.
If r ║ s and s║ t and l and m intersect, r, s,
and t, then

6. Theorem 8.7
If a ray bisects an angle of a triangle, then it divides the
opposite side into segments whose lengths are
proportional to the lengths of the other two sides.
If CD bisects ACB, then

7. Example 1: In the diagram, UY is parallel to VX, UV = 3, UW = 18, and XW = 16. What is the length of YX? U 3 18 V W 16 Y X YX = 3.2

8. Example 2: Given the diagram, determine whether PQ is parallel to TR
Example 2: Given the diagram, determine whether PQ is parallel to TR. Q P T R S Yes
If PQ is parallel to TR then the sides lengths would be in proportion.

9. HOMEWORK (Day 1)
pg. 502; 11 – 20

10. Example 3:
In the diagram 1  2  3, and PQ = 9, QR = 15, and ST = 11. What is the length of TU?

11. Example 4: In the diagram , LN = 15, LK = 3 and KN = 17
Example 4: In the diagram , LN = 15, LK = 3 and KN = 17. Use the given side lengths to find the length of MN. L M N K MN = 12.75

12. Example 5: FJ || GI. Find the values of the variables
Example 5: FJ || GI. Find the values of the variables. F 2 G 8 9 y H x I 12 J x = 9.6, y = 7.2

13. HOMEWORK (Day 2)
pg. 503; 21, 23, 25