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

SIDE-SPLITTER: Splits the sides into pieces whose ratios are proportional – does not work for the bases! (AE/EB = AF/FC ≠ EF/BC)

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

Check It Out! Example 1 Find PN.

Example 2: Verifying Segments are Parallel Verify that .

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.

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.

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

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

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

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

Lesson Quiz: Part III

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’

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 = $624,703 B = $750,594