1. Write the angles in order from 2. Write the side lengths in order from
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1 Lesson 1 Assignment Triangle Inequalities 1. Write the angles in order from 2. Write the side lengths in order from smallest to largest. shortest to longest. 3. Tell whether a triangle can have the sides with the given lengths. Explain. a. 6, 10, 15 b. 14, 18, 32 c. 11.9, 5.8, 5.8 d. 103, 41.9, The lengths of two sides of a triangle are given. Find the range of possible lengths for the third side. a. 4, 19 b. 28, 23 c. 9.2, The five steel tubes of a mountain bike frame form two triangles as shown. List the five tube lengths in order from shortest to longest. 6. The length of the base of an isosceles triangle is 15. What is the range of the possible lengths of each leg? 7. List the sides of each triangle in order from shortest to longest.
2 8. Compare lengths. Fill in the blanks with <, >, or =. a. QS PS b. PQ QS c. QS PR d. QS RS e. PQ RS d. RS PS 9. Compare angle measures. Fill in the blanks with <, >, or =. a. m ABE m BEA b. m CBE m CEB c. m DCE m DEC d. m DCE m CDE e. m ABE m EAB f. m EBC m ECB 10. Each set of expressions represents the lengths of the sides of a triangle. Find the range of possible values for n. a. n, 6, 8 b. 2n, 5, 7 c. n + 1, 3, 6
3 Lesson 2 Assignment Ratio and Proportion 1. The ratio of the side lengths of an isosceles triangle is 4:4:7, and its perimeter is 52.5 cm. What is the length of the base of the triangle? 2. The ratio of the angle measures in a triangle is 5:12:19. What is the measure of the largest angle? Solve each proportion. Show work and circle answer(s) y 4. x z m m y y x x 2 9. Given that 5y 25x, express the ratio of x to y in simplest form. 10. Given that 35b 21c, express the ratio b:c in simplest form. 11. Madurodam is a park in the Netherlands that contains a complete Dutch city built entirely of miniature models. One of the models of a windmill is 1.2 meters tall and 0.8 meters wide. The width of the actual windmill is 20 meters. What is its height?
4 12. During an NFL season, a football team wins 10 of their 16 games. What is the team s ratio of wins to losses in simplest form? 13. Given that a. 7a a 5 b 7, complete each of the following: b. b a c. a A Claymation film is shot on a set that a scale model of an actual city. On the set, a skyscraper is 1.25 inches wide and 15 inches tall. The actual skyscraper is 800 feet tall. a. Write a proportion that you can use to find the width of the actual skyscraper. b. Solve the proportion from part a. What is the width of the actual skyscraper? DOES YOUR ANSWER MAKE SENSE? WHY OR WHY NOT? 15.A photo shop makes prints of photographs in a variety of sizes. Every print has a length-towidth ratio of 5:3.5 regardless of its size. A customer wants a print that is 20 inches long. What is the width of this print?
5 Lesson 3 Assignment Similarity in Figures Identify the pairs of congruent angles and corresponding sides Determine whether the figures are similar. If so, write the similarity ratio and a similarity statement The ratio of a model car s dimensions to the actual car s dimensions is. The model has a length of 3 inches. What is the length of the actual car, in FEET AND INCHES? 1 56
6 Tell whether each statement is sometimes, always, or never true. 6. Two right triangles are similar. 7. Two squares are similar. 8. A parallelogram and a trapezoid are similar. 9. If two polygons are congruent, they are also similar. 10. If two polygons are similar, they are also congruent. Find the value of x A dining room is 18 feet long and 14 feet wide. On a blueprint for the house, the dining room is 3.5 inches long. To the nearest tenth of an inch, what is the width of the dining room on the blueprint? 14. Two similar polygons have a similarity ratio of 1:1. What can be concluded about the two polygons? Explain.
7 Lesson 4 Assignment Triangle Similarity Explain why the triangles are similar and write a similarity statement Verify that the given triangles are similar (hint: try drawing triangles separately) 5. The picture shows a person taking a pinhole photograph of himself. Light entering the opening reflects his image on the wall, forming similar triangles. What is the height of the image to the nearest tenth of an inch? Draw JKL and MNP. Determine if you can conclude that JKL MNP based on the given information. If so, which postulate or theorem justifies your response? JK KL JK KL JL JL KL 6. K N, J M, MN NP MN NP MP MP NP
8 Find the value of x ABC is NOT similar to JKL, and JKL is NOT similar to to XYZ XYZ? Why or why not? Make a sketch to illustrate your reasoning.. Could ABC be similar PQ QR 12. Draw and label PQR and STU such that 2 but PQR is NOT similar to ST TU STU. 13. Given that KNJ is isosceles with NK NJ, and H L, explain why GHJ MLK.
9 Lesson 5 Assignment Properties of Similar Triangles Find the length of each segment. Show work Verify that the given segments are parallel. Show work The wooden treehouse pictured has horizontal siding that is parallel to the base. What are the lengths of LM and MN, to the nearest hundredth of a foot? Show work.
![What are two possible lengths for the third side? [hint: try drawing a picture] 15. A developer is laying out lots along Grant Rd., whose total length is 500 feet.](/docs-images/77/74930993/images/10-4.jpg "Given the width of each of the three lots along Chavez St., what is the width of EACH of the lots along Grant Rd? Show work and round answers to the nearest foot. 16.")
10 Find the length of each segment. Show work In the figure, BC DE FG. Complete each proportion. AB AC 8. BD 9. AE 10. DF EG DF EG CE 11. AF AB 12. BD AC CE 13. EG AB BF AC 14. The bisector of an ANGLE of a triangle divides the opposite side of the triangle into segments that are 12 inches and 16 inches long. Another side of the triangle is 20 inches. What are two possible lengths for the third side? [hint: try drawing a picture] 15. A developer is laying out lots along Grant Rd., whose total length is 500 feet. Given the width of each of the three lots along Chavez St., what is the width of EACH of the lots along Grant Rd? Show work and round answers to the nearest foot. 16. Given that DE BC, XY AD, find EC.
11 Lesson 6 Assignment Indirect Measurement 1. Jenny is 5 ft 2 in tall. To find the height of a light pole, she measured both her shadow and the pole s shadow. Using the figure at the right, what is the height of the pole, in feet and inches? A park at the end of a city block is a RIGHT TRIANGLE with legs 150 feet and 200 feet long. Make a scale drawing (using a straightedge) of the park using the following scales in:100 ft 3. 1 in: 300 ft 4. 1 in:150 ft Given that pentagon ABCDE ~ pentagon FGHJK, find each of the following. 5. perimeter of pentagon FGHJK 6. area of pentagon FGHJK
12 Given: ABC DEF 7. If the ratio of the perimeter of ABC to the perimeter of DEF is of ABC to DEF? 8 9, what is the similarity ratio 8. If the ratio of the area of ABC to the area of DEF is to DEF? 16 25, what is the similarity ratio of ABC 9. If the ratio of the area of ABC to the area of DEF is to ABC? 4 81, what is the similarity ratio of DEF 10. The scale of a model of the Space Shuttle is 1 in:50 ft. In the actual shuttle, the main cargo bay measures 15 feet wide by 60 feet long. What are the dimensions of the cargo bay in the model? Given that PQR WXY, find each ratio. perimeter of PQR area of perimeter of WXY area of WXY PQR 13. Given that rectangle ABCD ~ rectangle EFGH. The area of rectangle ABCD is 135 in 2, and the area of rectangle EFGH is 240 in 2. If the width of rectangle ABCD is 9 inches, what is the length and width of rectangle EFGH? 14. Keisha is making two scale drawings of her school. In one drawing, she uses a scale of 1 cm:1 m, and in the other, she uses a scale of 1 cm:5 m. Which of these scales produces the smaller drawing? Explain. 15. The similarity of square ABCD to square EFGH is 4 9. Find the side lengths of each square. Show work.
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