1. Proportional Lengths
Unit 6: Section 7.6

2. Theorem 7-3 Triangle Proportionality Theorem
Divided Proportionally : If points L and M lie on and and
, then and are divided proportionally.
A L B C M D
Theorem Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally.
Then T P Q R S

3. Use the Triangle Proportionality Theorem to justify any proportion equivalent to
For the diagram, some of the proportions that can be justified are: c a j k b d

4. Example 1: =
If CD = 3, DA = 6, and DE = 3.5, then
AB = _________
c. If CB = 12, EB = 8, and CD = 6, then DA = __________
Practice 1:
True or false?
a. b.
c. d.
e. f. B A
10.5 E D 12 C
True
True
True
False
False
True

5. Practice 2: Find the value of x.
Corollary : If three parallel lines intersect two transversals, then they divide the transversals proportionally. If
then
Ans: 4 x 8 1 2 R X S Y T Z

6. Example 2
If a = 2, b = 3, and c = 5,
then d = _________
If a = 4, b = 8, c = 5,
then c + d = _________
Practice 3
1.True or false?
a. b.
c. d.
2. Find the value of x. a c
7.5 b d 15 a c T F b d F F 5 x
45/7 7 9

7. Theorem 7-4
Triangle Angle-Bisector Theorem: If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other sides.
Example 3 F G E D x 10 12
12x -120 = 240 24
12x = 360
x = 30

8. Practice 4
Find the value of x.
If time: Additional Practice p272 #3-11 odd
Homework: Practice Worksheet 7.6 8
Ans: x = 12 14 x 21