1. Proportions in Triangles Chapter 7 Section 5

2. Objectives Students will use the Side-Splitter Theorem and the Triangle-Angle- Bisector Theorem

3. Question? How do you know if two triangles are similar?

4. Remember When two or more parallel lines intersect other lines, proportional segments are formed.

5. Side Splitter Theorem (7-4) If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally (creates two proportional triangles).

6. Turn to page 472… Look at Problem 1 Try the “Got It” problem for that example.

7. Question What condition of the Side-Splitter Theorem is marked in the diagram for Problem 1? In other words, what is marked in the figure that lets us know we can use the Side-Splitter Theorem?

8. Corollary to the Slide-Splitter Theorem parallel If three parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional. A B C D E F

9. On Page 473… Look at Problem 2 Try the “Got It” for this example

10. Question: Should the numerators and the denominators of each ratio in the proportion be corresponding sides of the figure?

11. Triangle-Angle-Bisector Theorem (7-5) 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. A B C D ADAB DC=CB

12. On page 474 Look at Problem 3

13. Question Using the diagram for Problem 3, and considering the properties of proportions, how can the proportion be rewritten so that the x is in a numerator?

14. On page 474… Try problems #1-8 on your own.

15. Exit Slip/Reflection 1.What is the Side-Splitter-Theorem? 2.What is the Triangle-Angle-Bisector Theorem? 3.Give an example of each.