Skills Practice Skills Practice for Lesson 5.1

Transcription

1 Skills Practice Skills Practice for Lesson.1 Name Date Ace Reporter Review of Ratio and Proportion Vocabulary Match each definition to its corresponding term. 1. a and d in a c b d a. ratio 2. b and c in a c b d b. probability 3. a comparison of two or more numbers that uses division c. proportion 4. an equation that states that two ratios are equal d. means. the ratio of the number of successful outcomes to e. extremes the number of possible outcomes Problem Set Write each ratio as a simplified fraction. Then write each ratio using a colon. 1. If 7 students in one class have pets and 18 do not, what is the ratio of the number of students who have pets to the total number of students? students 2 students 7 students : 2 students 2. This season, Mia s soccer team won 9 games and lost games. What is the ratio of the number of games Mia s team won to the total number of games that the team played? Chapter Skills Practice 46

2 3. In a survey of 10 people, 87 said that they enjoy comedies. What is the ratio of the number of people who like comedies to the number of people who participated in the survey? 4. If 40 out of 240 students are in the school marching band, what is the ratio of the number of students in the marching band to the total number of students?. A display at a bookstore holds 1 fiction books and 10 nonfiction books. What is the ratio of fiction books to nonfiction books? 6. In a board game, 20 of the tokens are red, 20 are blue, and 20 are green. What is the ratio of blue tokens to red tokens? Write and simplify each ratio. 7. In an art class, 12 students report that drawing is their favorite medium. If there are 18 students in the class, what is the ratio of students who prefer drawing to the total number of students? students 3 students 2 students : 3 students 8. A survey found that 4 participants prefer to read the news online and 20 participants prefer to read printed newspapers. What is the ratio of people who prefer to read the news online to those who prefer to read newspapers? 466 Chapter Skills Practice

3 Name Date 9. In one issue of a magazine, 81 pages contained illustrations such as photographs. If the magazine issue had 108 pages, what is the ratio of pages with illustrations to pages without illustrations? 10. A gardening store sells seed packets. Each packet contains several kinds of pepper seeds. Thirty-six of the seeds in one packet are red pepper seeds. If the packet contains 100 seeds, what is the ratio of red pepper seeds to other kinds of pepper seeds? Write an equation or inequality comparing the ratios. 11. An orchard has 80 apple trees and 60 peach trees. Analyze the orchard s mix of fruit trees. Does the orchard have a higher ratio of apple trees to the total number of trees? Or does the orchard have a higher ratio of peach trees to the total number of trees? apple trees 140 trees peach trees trees 80 apple trees 60 peach trees 140 trees 140 trees The orchard has a higher ratio of apple trees to the total number of trees. 12. At an animal shelter, 64 of the 100 animals are cats. The rest of the animals at the shelter are dogs. Analyze the shelter s mix of animal types. Does the animal shelter have a higher ratio of cats to the total number of animals? Or does the shelter have a higher ratio of dogs to the total number of animals? Chapter Skills Practice 467

4 13. Jorge s baseball team won 12 games and tied 3 games. They played 20 games that season. Which ratio is greater: the ratio of games won to games tied, or the ratio of games won to the total number of games? 14. In a board game, 2 tiles have vowels marked on them and the remaining 3 tiles have consonants. Which ratio is higher: the ratio of vowel tiles to consonant tiles, or the ratio of vowel tiles to the total number of tiles? Solve each proportion. 1. The scale on a map of a state park is 2 inches : 00 meters. The Visitor Center is 3. inches on the map from the waterfall. How many meters is the walk from one to the other? x 2 x x 87 The waterfall is 87 meters from the Visitor Center. 468 Chapter Skills Practice

5 Name Date 16. A county map has a scale of 2 inches : 3 miles. If two towns are 7 inches apart on the map, what is the actual distance between the towns? 17. A recipe that makes 3 dozen rolls calls for 4 ounces of butter. How many ounces of butter would be needed to make 108 rolls? 18. A bakery can produce 28 trays of muffins in four hours. How long would it take the bakery to produce 98 trays? Write and solve a proportion to answer each question. 19. A biology class counts 896 insects in a 100-square-meter area of a city park. The whole park measures 000 square meters. If the ratio is the same throughout the park, how many insects would you predict are in the whole park? x x 4,480,000 x 44,800 There would be about 44,800 insects in the city park. Chapter Skills Practice 469

6 20. In Joan s survey of 240 participants, 210 said that they recycle. A second survey by Shao finds the same ratio of people who recycle, but this second survey finds that 2800 participants report that they recycle. How many people would you predict participated in the second survey by Shao? 21. Twenty-three out of 0 people who go to the Roxy movie theater on Thursdays buy popcorn. Each week 30 people visit the Roxy. If the ratio of those who buy popcorn to total patrons is the same each night, how many people would you predict buy popcorn each week? 22. During one day, 88 customers at Wholesome Foods grocery store brought reusable shopping bags, while 64 customers did not. If the store has 1064 customers each week, how many customers would you predict bring reusable bags during one week? 470 Chapter Skills Practice

7 Skills Practice Skills Practice for Lesson.2 Name Date Picture Picture on the Wall Similar Polygons Vocabulary Define each term in your own words. 1. similar polygons 2. scale model 3. scale Problem Set Determine whether each pair of figures is similar. Explain your answer in. 6 in. 3 in. 3 in. 3 in. 6 in. The figures are similar. The ratios of the side lengths are 1 : 2 for all sides of the triangle. The angles are congruent because both triangles are equilateral and all angles are equal to 60. Chapter Skills Practice 471

8 2. 9 cm 2 cm 6 cm 3 cm 3. 4 m 4 m 4 m 4 m Given each pair of similar figures, identify all pairs of corresponding sides.. A 3 cm C 7 cm AB and DE AC and DF BC and EF B E 7 cm F 3 cm D 6. J G H 7º 7º 0º 0º I K L 472 Chapter Skills Practice

9 Name Date 7. E A D 100º H 8. I 1 in. L M 12 in. P B 60º C F 60º 100º G 3in. J in. 4 in. K 3in. N 9 in. 1 in. O Given each pair of similar figures, identify each pair of corresponding angles. 9. ABC EFD 10. GHI KLJ D J A E G B C F H I K L A and E B and F C and D 11. ABCD HGFE 12. IJKL NMPO F I A D E J K B C H G L M P O N Chapter Skills Practice 473

10 Given each pair of similar figures, determine the length of the unknown side, x º 8 cm 0º 6 cm 9 cm 0º x 40º 14. ABCD EFGH B 16 mm C A 28 mm D H x E G 8 mm F x x 72 x 12 cm 1. x 3 ft ft 2 ft in in in. 32 in. 7 x in. Given each pair of similar figures, determine the measure of the unknown angle, x. 17. ABC EFD 18. ABCD HGFE A 80 B C F E x D A 130 D 100 B 8 C H E x G F D C m D m C m D 40º 474 Chapter Skills Practice

11 Name Date 19. GHI KLJ 20. IJKL NMPO G J x I 7 L M N H I K L J 13 K P x O Determine the unknown measure. 21. An artist crafts a scale model of a sculpture that he is planning to carve. The scale of the model is 12 : 1. If the height of the model is 1 inches, what will be the height of the sculpture? x x 180 The height of the sculpture will be 180 inches. 22. A graphic designer creates a scale model of a new action figure. The scale of the model is : 2. If the height of the model is 4 inches, what will be the height of the action figure? 23. A civil engineer built a scale model of a bridge that needs repair. The scale of the model is 2 : 1. If the length of the bridge is 10 feet, what is the length of the model? Chapter Skills Practice 47

12 24. An architect must create a scale model of a skyscraper that she is proposing. The scale of the model is 120 : 1. If the height of the skyscraper will be 420 feet, what should be the height of the model? Use the given information to answer each question. 2. The ratio of the side lengths of two similar triangles is 3. What is the ratio of the 1 perimeters of the triangles? The ratio of the perimeters of the triangles is 3 because it is the same as the 1 ratio of the side lengths. 26. The ratio of the side lengths of two similar pentagons is 3. What is the ratio of the perimeters of the pentagons? 27. The ratio of the side lengths of two similar rectangles is 4. What is the ratio of the 3 areas of the rectangles? 28. The ratio of the side lengths of two similar hexagons is 2. What is the ratio of the 7 areas of the hexagons? 476 Chapter Skills Practice

13 Skills Practice Skills Practice for Lesson.3 Name Date To Be or Not To Be Similar? Similar Triangle Postulates Vocabulary Give an example of each term. Include a sketch with each example. 1. Angle-Angle Similarity Postulate 2. Side-Side-Side Similarity Postulate Chapter Skills Practice 477

14 3. Side-Angle-Side Similarity Postulate 4. included angle. included side 478 Chapter Skills Practice

15 Name Date Problem Set Explain how you know that each pair of triangles are similar. 1. Two angles of one triangle are congruent to the corresponding angles of the other triangle. This fact satisfies the Angle-Angle Similarity Theorem ft 3 ft 4. ft 4. ft 2 ft 3 ft 4. 4 in. 4 in. in. 8 in. 10 in. 8 in. Chapter Skills Practice 479

16 . 2 cm 60 3 cm 9 cm 60 6 cm 6. mm 40 7 mm 14 mm 10 mm 40 Determine what additional information you would need to prove that each pair of triangles are similar using the given theorem. 7. What information would you need to use the Angle-Angle Similarity Theorem to prove that the triangles are similar? 3 60 If you know that one of the angle measures in the first triangle is 60 degrees and that one of the angle measures in the second triangle is 3 degrees, then you can use the theorem directly. If you know the measure of at least one other angle in each triangle, then you can use the theorem after first proving other steps. 480 Chapter Skills Practice

17 Name Date 8. What information would you need to use the Angle-Angle Similarity Theorem to prove that the triangles are similar? What information would you need to use the Side-Angle-Side Similarity Theorem to prove that the triangles are similar? 6 m 4 m 10 m 10. What information would you need to use the Side-Angle-Side Similarity Theorem to prove that the triangles are similar? in. 9 in. in. 9 in. Chapter Skills Practice 481

18 11. What information would you need to use the Side-Side-Side Similarity Theorem to prove that these triangles are similar? 12 cm 6 cm cm 14 cm 12. What information would you need to use the Side-Side-Side Similarity Theorem to prove that these triangles are similar? 4 ft 6 ft Determine whether each pair of triangles is similar. Explain your reasoning. 13. Y 10.8 yd T R 10 yd 6 yd S X 18 yd Z XY 10 RS 6 3, XZ 18 RT 10.8, and the included angles X and R are congruent, 3 so the triangles are similar by the Side-Angle-Side Similarity Postulate. 482 Chapter Skills Practice

19 Name Date 14. K B 9 cm 6 cm 8 cm 12 cm J 12 cm L A 16 cm C 1. N 60 3 in. 2 in. M O Q in. in. R P 16. P Q T R 100 S 60 U Chapter Skills Practice 483

20 17. V 10 m W 18 m X A 4. m B 2. m C 18. K 3 ft ft J 6 ft L I 10 ft 12 ft H 7 ft G 484 Chapter Skills Practice

21 Name Date 19. M O N P R Q 20. D 1 m 18 m E 27 m F S 36 m 24 m U T 20 m Chapter Skills Practice 48

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23 Skills Practice Skills Practice for Lesson.4 Name Date Triangle Side Ratios Angle Bisector/Proportional Side Theorem Vocabulary Define the term in your own words. 1. Angle Bisector/Proportional Side Theorem Problem Set Calculate the length of the indicated segment in each figure. 1. HJ bisects H. Calculate FH. 2. LN bisects L. Calculate MN. F 1 cm J 18 cm G 8 in. L in. FH FH 31 FH 17. cm H 21 cm K 4 in. N M Chapter Skills Practice 487

24 3. BD bisects B. Calculate AD. 4. SQ bisects S. Calculate PS. B 3 ft C 2 ft P 9 m Q 12 m 6 ft D S 18 m R A. YZ bisects Y. Calculate YW. 6. VX bisects V. Calculate XW. 4 cm Y U 9 ft V X 8 cm Z 9 cm W 10 ft X 6 ft W 488 Chapter Skills Practice

25 Name Date 7. GE bisects G. Calculate DF. D 8. ML bisects M. Calculate LN. N cm 1 cm E L 11 mm G 18 cm F K mm 4 mm M Use the given information to answer each question. 9. On the map shown, Willow Street bisects the angle formed by Maple Avenue and South Street. Mia s house is miles from the school and 4 miles from the fruit market. Rick s house is 6 miles from the fruit market. How far is Rick s house from the school? Maple Avenue Mia s house School Willow Street Fruit market South Street Rick s house River Avenue x 4 6 4x 30 x 7. Rick s house is 7. miles from the school. Chapter Skills Practice 489

26 10. Jimmy is hitting a golf ball towards the hole. The line from Jimmy to the hole bisects the angle formed by the lines from Jimmy to the oak tree and from Jimmy to the sand trap. The oak tree is 200 yards from Jimmy, the sand trap is 320 yards from Jimmy, and the hole is 20 yards from the sand trap. How far is the hole from the oak tree? Jimmy Oak tree Hole Sand trap 11. The road from Central City on the map shown bisects the angle formed by the roads from Central City to Minville and from Central City to Oceanview. Central City is 12 miles from Oceanview, Minville is 6 miles from the beach, and Oceanview is 8 miles from the beach. How far is Central City from Minville? Beach Minivilte Oceanview Central City 490 Chapter Skills Practice

27 Name Date 12. Luigi is racing a remote control car from the starting point to the winner's circle. That path bisects the angle formed by the lines from the starting point to the house and from the starting point to the retention pond. The house and the retention pond are each 00 feet from the starting point. The house is 720 feet from the retention pond. How far is the winner's circle from the retention pond? Starting point House Winner s circle Retention pond Chapter Skills Practice 491

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29 Skills Practice Skills Practice for Lesson. Name Date Geometric Mean Similar Right Triangles Vocabulary Write the term from the box that best completes each statement. Right Triangle/Altitude Similarity Theorem geometric mean Right Triangle Altitude Theorem 1 Right Triangle Altitude Theorem 2 1. The states that if an altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. 2. The states that if the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the measure of the hypotenuse and the measure of the segment of the hypotenuse adjacent to the leg. 3. The of two positive numbers a and b is the positive number x such that a x x b. 4. The states that the measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse. Problem Set Construct an altitude to the hypotenuse of each right triangle. 1. K 2. O M J L N Chapter Skills Practice 493

30 3. 4 U Q S R T V Use each similarity statement to write the corresponding sides of the triangles as proportions.. CGJ MKP 6. XZC YMN CG MK GJ KP CJ MP 7. ADF GLM 8. WNY CQR Use the Right Triangle/Altitude Similarity Theorem to write three similarity statements involving the triangles in each diagram. 9. G Q H P 10. M P R Z HPG PQG, HPG HQP, PQG HQP 494 Chapter Skills Practice

31 Name Date 11. N K 12. W L T U M N Solve for x. 13. R x B 20 cm T 14. D 8 cm x A 6 in. F 6 in. G F FB TB RB FB 8 x x 64 x 3.2 cm 1. M x Z 16. R 9 in. S N 4 cm 12 cm P 6 in. Q x V Chapter Skills Practice 49

32 17. B 4 m D T 18. G K x 4 mi L 2 mi 10 m x F L Solve for x, y, and z. 19. W C CP WP 2 x WP PH x 4 x x 10 2 y x P 4 z H x y y 2 72 y 2 29 y 4 2 x 2 z z z z 496 Chapter Skills Practice

33 Name Date 20 B 3 V x y 1 R z Y 21. K z 8 y L 4 N x P Chapter Skills Practice 497

34 22. K H 4 x y A z T Use the given information to answer each question. 23. You are on a fishing trip with your friends. The diagram shows the location of the river, fishing hole, camp site, and bait store. The camp site is located 200 feet from the fishing hole. The bait store is located 110 feet from the fishing hole. How wide is the river? Bait store Camp site Fishing hole River x 200x 12,100 x 60. The river is 60. feet wide. 498 Chapter Skills Practice

35 Name Date 24. You are standing at point D in the diagram looking across a bog at point B. Point B is 84 yards from point A and 189 yards from point C. How wide across is the bog? A B Bog D C 2. Marsha wants to walk from the parking lot through the forest to the clearing, as shown in the diagram. She knows that the forest ranger station is 14 feet from the flag pole and the flag pole is 30 feet from the clearing. How far is the parking lot from the clearing? Clearing Forest ranger station Flag pole Parking lot Forest Chapter Skills Practice 499

36 26. Andre is camping with his uncle at one edge of a ravine. The diagram shows the location of their tent. The tent is 1.2 miles from the fallen log and the fallen log is 0.7 miles from the observation tower. How wide is the ravine? Tent Ravine Observation tower Fallen log 00 Chapter Skills Practice

37 Skills Practice Skills Practice for Lesson.6 Name Date Indirect Measurement Application of Similar Triangles Vocabulary Provide an example of the term. 1. indirect measurement Problem Set Explain how you know that each pair of triangles are similar. 1. A B C D E The angles where the vertices of the triangle intersect are vertical angles, so angles ACB and ECD are congruent. The angles formed by BD intersecting the two parallel lines are right angles, so they are also congruent. So by the Angle-Angle Similarity Theorem, the triangles formed are similar. Chapter Skills Practice 01

38 2. F G H I J 3. 6 in. 3 in. 8 in. 4 in. 4. B A D C E 02 Chapter Skills Practice

39 Name Date Use indirect measurement to calculate the missing distance.. Elly and Jeff are on opposite sides of a canyon that runs north to south. They want to know how wide the canyon is. Each person stands 10 feet from the edge. Then Elly walks 24 feet north, and Jeff walks 360 feet south. 24 ft 10 ft 10 ft 360 ft What is the width of the canyon? 10 x x 10 x 140 The distance across the canyon is 140 feet. 6. Zoe and Ramon are hiking on a glacier. They become separated by a crevasse running east to west. Each person stands 9 feet from the edge. Then Zoe walks 48 feet east, and Ramon walks 12 feet west. 48 ft 9 ft 9 ft 12 ft What is the width of the crevasse? Chapter Skills Practice 03

40 7. Minh wanted to measure the height of a statue. She lined herself up with the statue s shadow so that the tip of her shadow met the tip of the statue s shadow. She marked the spot where she was standing. Then she measured the distance from where she was standing to the tip of the shadow, and from the statue to the tip of the shadow. ft 84 ft 12 ft What is the height of the statue? 8. Dimitri wants to measure the height of a palm tree. He lines himself up with the palm tree s shadow so that the tip of his shadow meets the tip of the palm tree s shadow. Then he asks a friend to measure the distance from himself to the tip of his shadow and the distance from the palm tree to the tip of its shadow. 6 ft 11.2 ft 4 ft What is the height of the palm tree? 04 Chapter Skills Practice

41 Name Date 9. Andre is making a map of a state park. He finds a small bog, and he wants to measure the distance across the widest part. He first marks the points A, C, and E. Andre measures the distance from point A to C and from point A to E. Andre also marks point B along AC and point D along AE, such that BD is parallel to CE. A B 14 ft D 12 ft 126 ft C E What is the width of the bog at the widest point? 10. Shira finds a tidal pool while walking on the beach. She wants to know how wide it is. Using indirect measurement, she begins by marking the points A, C, and E. Shira measures the distance from point A to C and from point A to E. Next, Shira marks point B along AC and point D along AE, such that BD is parallel to CE. A C B 7 ft D 3 ft E 31. ft What is the distance across the tidal pool at its widest point? Chapter Skills Practice 0

42 11. Keisha is visiting a museum. She wants to know the height of one of the sculptures. She places a small mirror between herself and the sculpture, then she backs up until she can see the top of the sculpture in the mirror ft 13.2 ft. ft What is the height of the sculpture? 12. Micah wants to know the height of his school. He places a small mirror on the ground between himself and the school, then he backs up until he can see the highest point of the school in the mirror. 6 ft 93. ft 12.7 ft What is the height of Micah s school? 06 Chapter Skills Practice