This document discusses proportional relationships in triangles and solving proportions. It contains theorems about parallel lines intersecting two sides of a triangle proportionally and a ray bisecting an angle proportioning the sides. It also contains examples of using proportions to solve for variables in triangles and showing lines are parallel. The final sections provide homework problems from specific textbook pages.

1. 8.6 Proportion and Similar
Triangles

2. Theorem
Triangle Proportionality Theorem
If a line is parallel to one side of a
triangle and intersects the other two
sides, then it divides the two sides
proportionally.
EC
AE
DB
AD
=

3. Converse of the Triangle
Proportionally Theorem
If a line divides two sides of a triangle
proportionally, then the line is parallel
to the remaining side.
BCDE
EC
AE
DB
AD
//→=

4. Theorem
If three parallel lines are intersected by
two lines, then the lines are divided
proportionally.

5. Theorem
If a ray bisects one angle of a triangle,
then it divides the sides proportional
with the sides they are touching.

6. Solve for x

7. Solve for x
xx
x
=→=→= 36)9(2
96
2

8. Show that DE // BC
975.9
2426

9. Show that DE // BC
975.9
2426
BCDE
EC
AE
DB
AD
//→=

10. Solve for x
96
8
x

11. Solve for x
96
8
x
x
x
x
=
=
=
3
1
5
948
89
6

12. Solve for x
20
15
17
x

13. Solve for x
20
15
17
x
( )
7
2
7
25535
1525520
171520
20
17
15
=
=
−=
−=
−
=
x
x
xx
xx
xx

14. Homework
Page 502 – 503
# 11 - 28

15. Homework
Page 503 – 505
# 29 – 31,
34 – 37, 39,
41 – 50