Side Splitting Theorem 8.4

Identify parallel lines in triangles. homework Learn the side splitting theorem. Use the side splitting theorem to solve problems.

The Side Splitting Theorem Converse of the Side Splitting Theorem homework

Multiple Transversal Proportionality Corollary homework

Find the Length of a Side homework In  RST, RT||VU, SV = 3, VR = 8, and UT = 12. Find SU.

homework In  EBD, AC||ED, AE = 2, BA = 6, and AC = 9. Find ED. Find the Missing Measure using the Parallel Side 6x = 72 x = 12 A B C DE

homework In  ABC, XY||AC, AX = 4, XB = 10.5, and CY = 6. Find BY. Find the Length of a Side 10.5(6) = 4x 63 = 4x x = YC BY XA BX 

homework The lines are parallel. Find x. 13x = 44

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. homework 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 homework

∆ABE ~ ∆ACD, find CD. homework 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. homework Let BF be represented by x. 24x = 6.5x x = x  6.3

homework 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. 24x = 15(8) 24x = 120 x = 5

Find x and y. Congruent Segments homework 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. x = 6; y = 3

homework 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. homework

 ABE ~  ACD find BE and CD. homework 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? homework 1.5x = x  196 ft

homework The triangles are similar. Find x, the distance across the lake. 90x = 19,800 x = 220 yards

homework Find x and y. 7.2x = 72 x = 10 yards x y 8y = y = 5.76 yards

homework The triangles are similar. Find b, the brace of the ladder. 28b = 336 x = 12 inches

homework Find the height of the tree. 8x = 170

homework In Washington D.C. 17 th, 18 th, 19 th and 20 th streets are parallel streets that intersect Pennsylvania Ave and I St. a. How long is Pennsylvania Ave between 19 th St and 18 th St? b. How long is Pennsylvania Ave between 18 th St and 17 th St? 380x = x =

homework Find x. a. b. 24x 2 – 40x = 20x x 4x 2 – 80x = 0 4x(x – 20) = 0 x = 0 or x = 20 x 2 + x = x 2 – 3x + 6x – 18 x 2 + x = x 2 + 3x – 18 x = 3x – 18 –2x = –18 x = 9

Assignment 8.4 Side Splitting