1. 8.4 Proportionality Theorems and Applications
“Side Splitter”
Triangle Angle Bisector

2. SIDE-SPLITTER: Splits the sides into pieces whose ratios are proportional – does not work for the bases! (QT/TR = SU/UR ≠ QS/TU)

3. Example 1: Finding the Length of a Segment
Find US using Side-Splitter and
by using ROCSAP.

4. Check It Out! Example 1
Find PN.

6. Example 2: Verifying Segments are Parallel
Verify that

7. For multiple parallel lines the ratio of ANY two segments on one side will be proportional to the corresponding ratio of two segments on the other side.

8. Example 3: Art Application
Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.

9. NOTE: The triangles are not similar!
You can NOT do a proportion for the
angle bisector segment

10. Example 4: Using the Triangle Angle Bisector Theorem
Find PS and SR.
Find AC and DC.

11. Find the lengths of each segment. 1. JG and HJ 2. SR and ST
Lesson Quiz: Part I
Find the lengths of each segment.
1. JG and HJ 2. SR and ST 60

12. Lesson Quiz: Part II
3. Verify that BE and CD are parallel.

13. Lesson Quiz: Part III

14. Lesson Quiz: Part IV A
The real estate term beach frontage refers to
the length of the property along the ocean.
Find the beach frontage for each lot
rounded to the nearest tenth of a foot.
a = 52.6’, b = 63.2’, c = 84.2’

15. Lesson Quiz: Part IV B
In general, the price of an ocean-front lot
is based on the amount of beach frontage.
Assuming the prices are proportional and
lot C sells for $1 million, what would lots
A and B sell for?
A = $624, B = $750,594