1. Proportions and Similar Triangles
Geometry
Unit 11, Day 8
Ms. Reed

2. Proportions and Similar Triangles
We will be investigating ways proportional relationships in triangles
You will need:
Paper
Ruler
Protractor
Calculator

3. On your paper: Construct a triangle, label it ABC
Create a line parallel to AC. Call the intersection point on AB, D and the point on BC, E.
Measure DB, DA, BE, and EC
Compare the ratios of BD/DA and BE/EC
WHAT DO YOU NOTICE?

4. Conclusion
If a line is parallel to one side of the triangle and intersects the other two sides, then it divides those sides proportionally.
This is called the Side-Splitter Theorem

5. Example 1
Set up the proportion
x =8 x 5 16 10

6. Example 2
Solve for x
x = 1.5 5 3
2.5 x

7. On your paper: Create 3 Parallel Line
Draw 2 transversals through the lines so it looks like this:
Label as shown a c b d

8. What do you notice? Measure a, b, c and d.
Compare the relationship between a/b and c/d.
WHAT DO YOU NOTICE?

9. What we discovered!
If 3 parallel lines intersect two transversals, then the segments intercepted on the transversals are proportional.

10. Example 3 y
16.5 15 25 x 30
x =18 y = 27.5

11. Sail Making!
When making a boat sail, all of the seams are parallel. Find the missing variables
x = 2 ft, y=2.25 ft
1.5ft
2ft
1.5ft y x
1.5ft
3ft
2ft

12. On your paper Create a new triangle and label it ABC Measure A
Bisect A by drawing an angle with half its measure.
Label the intersection point with the CB and the bisecting line point D
Compare the ratios of CD/DB and CA/BA
WHAT DID YOU NOTICE?

13. Conclusion
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.
This is called the Triangle-Angle-Bisector Theorem.

14. Example 4
Set up the proportion
x=9.6 P 8 Q x 5 S R 6