Side Splitting Theorem Side Splitting Theorem 8.48.4

• Identify parallel lines in triangles.

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• Learn the side splitting theorem.

• Use the side splitting theorem to solve problems.

The Side Splitting TheoremThe Side Splitting Theorem

Converse of the Side Splitting TheoremConverse of the Side Splitting Theorem

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Multiple Transversal Proportionality CorollaryMultiple Transversal Proportionality Corollary

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Find the Length of a SideFind the Length of a Side

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In RST, RT||VU, SV = 3, VR = 8, and UT = 12. Find SU.

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In EBD, AC||ED, AE = 2, BA = 6, and AC = 9. Find ED. Find the Missing Measure using the Parallel SideFind the Missing Measure using the Parallel Side

.ED

BE

AC

BA

x

8

9

6

6x = 72

x = 12

A

B

C

DE

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In ABC, XY||AC, AX = 4, XB = 10.5, and CY = 6. Find BY.

Find the Length of a SideFind the Length of a Side

64

510 x

.

10.5(6) = 4x

63 = 4x

x = 15.75

.YCBY

XABX

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The lines are parallel. Find x.

13

4

11

x

13x = 44

13

53x

Explain why ∆RSV ~ ∆RTU and then find RT.

Prove triangles are similar.

It is given that S T. R R by Reflexive Property.

Therefore ∆RSV ~ ∆RTU by AA Similarity.

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RT(8) = 10(12)

8RT = 120

RT = 15

In the figure, Larch, Maple, and Nuthatch Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.

Proportional Segments

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∆ABE ~ ∆ACD, find CD.

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x(9) = 5(3 + 9)

9x = 60

AC || FG. ∆ABC ~ ∆FBG. Find BA to the nearest tenth of a foot.

Therefore, BA = 23.3 ft. homeworkhomework

Let BF be represented by x.

24

17x

5.6

x

24x = 6.5x + 110.5

17.5x = 110.5

x 6.3

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In the figure, Davis, Broad, and Main Streets are all parallel. The figure shows the distances in city blocks that the streets are apart. Find x.

x

15

8

24

24x = 15(8)

24x = 120

x = 5

Find x and y.Congruent Segments

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The segments with lengths 5y and are congruent since parallel

lines that cut off congruent segments on one transversal cut off

congruent segments on every transversal.

7y3

8

x = 6; y = 3

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Determine if the sides are parallel.a. b.

c. d.

Yes sides are proportional 3:5. Yes sides are proportional 5:4.

No sides aren’t proportional. Yes sides are proportional 7:5.

Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower?Since the sun’s rays form similar triangles,

the following proportion can be written.

The Sears Tower is 1452 feet tall. homeworkhomework

ABE ~ACD find BE and CD.

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6x

5.7

x

3

3x + 18 = 7.5x

4.5x = 18

x = 4

1. A

2. B

3. C

4. D

On her trip along the East coast, Jen stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina.At that particular time of day, Jen measures her shadow to be 1 feet 6 inches in length and the length of the shadow of the lighthouse to be 53 feet 6 inches. Jen knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot?

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x

5.53

5.5

5.1

1.5x = 294.25

x 196 ft

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The triangles are similar. Find x, the distance across the lake.

x

180

110

90

90x = 19,800

x = 220 yards

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Find x and y.

927

8 x

.

7.2x = 72

x = 10 yardsx

y

y

46

27

8 .

.

8y = 46.08

y = 5.76 yards

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The triangles are similar. Find b, the brace of the ladder.

21

2816

b

28b = 336

x = 12 inches

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Find the height of the tree.

x

34

5

8

8x = 170

feet4

121x

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In Washington D.C. 17th, 18th, 19th and 20th streets are parallel streets that intersect Pennsylvania Ave and I St.

a. How long is Pennsylvania Ave between 19th St and 18th St?

b. How long is Pennsylvania Ave between 18th St and 17th St?

x

500

425

380

380x = 212500

.ft2.559x

x

600

425

380 380x = 255000 .ft1.671x

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Find x.a. b.

10x6

8x4

x5

x4

24x2 – 40x = 20x2 + 40x4x2 – 80x = 04x(x – 20) = 0

x = 0 or x = 20

1x

3x

6x

x

x2 + x = x2 – 3x + 6x – 18 x2 + x = x2 + 3x – 18 x = 3x – 18 –2x = –18

x = 9

AssignmentAssignment

8.4 Side Splitting8.4 Side Splitting