Additional Practice. Name Date Class. 1. Refer to the rectangle at the right for the exercises below.

Transcription

1 Additional Practice Investigation 1 1. Refer to the rectangle at the right for the eercises below. a. Give the length and width of a larger similar rectangle. Eplain your reasoning. cm cm b. Give the length and width of a smaller similar rectangle. Eplain your reasoning. c. Give the length and width of a rectangle that is not similar to this one. Eplain your reasoning. 55

2 Additional Practice (continued) Investigation 1 2. Figure VWXYZ is an enlargement of figure ABCDE. Name all the pairs of corresponding sides and all the pairs of corresponding angles of the two figures. Y E A Z X D C B V W. a. Draw a square. Then draw a square with a side length that is twice the side length of the original square. How many copies of the smaller square will fit inside the larger square? b. Will you get the same answer for part (a) no matter what side length you choose for the original square? Eplain your reasoning. 56

3 Additional Practice (continued) Investigation 1. a. Carl made shape B by making a photocopy of shape A. What percent did he enter in the copier? Shape A Shape B b. Amy made a photocopy of shape A by entering 250% into the photocopier. Sketch the copy she got. 57

4 Additional Practice: Digital Assessments Investigation 1 5. Figure ABCDEF is similar to figure UVWXYZ. Which of the following statements are definitely true? Select all that apply. E F D A C B Y Z X U V W 6. Which of the following are equivalent to 5 8? Select all that apply. 10 n 16 7 n n 2 n n n Angle A corresponds to angle U. n Angle C is congruent to angle W. n Angle B corresponds to angle Y. n Side DE corresponds to side XY. n Side FE is the same length as side WX. 7. Use the tiles to show one way to find 0% of

5 Skill: Using Percent Investigation 1 Find the given percent of each number. Show your work % of % of % of 50. 0% of % of % of % of % of % of

6 Additional Practice Investigation 2 1. Draw any rectangle that is not a square. Draw a similar rectangle by applying a scale factor of to the original rectangle. a. How many copies of the original rectangle will fit inside the new rectangle? b. Will you get the same answer for part (a) no matter what rectangle you use as the original rectangle? 60

7 Additional Practice (continued) Investigation 2 2. Make a figure by connecting the following sets of points on the coordinate grid: Set 1: (8, 5), (8, 8), (0, 8), (0, 5), (8, 5) Set 2: (, 6), (8, 2), (0, 2), (, 6) Set : (2, 6), (1, 6), (1, 7), (2, 7), (2, 6) Set : (6, 6), (7, 6), (7, 7), (6, 7), (6, 6) a. Suppose you used the rule (6,6y) to transform this figure into a new figure. How would the angles of the new figure compare with the angles of the original? How would the side lengths compare? Would the new figure be similar to the original? Eplain. b. Suppose you used the rule ( 1, y ) to transform the original figure into a new figure. Would the new figure be similar to the original? Eplain. 61

8 Additional Practice (continued) Investigation 2. Recall that Zug Wump was made from Mug Wump using a scale factor of 2. What is the scale factor from Zug to Mug? Eplain.. a. Wendy drew a very large Wump using the rule (8,8y). She said that the scale factor from Mug to her Wump was 8 and that the scale factor from Zug to her Wump was. Do you agree with Wendy? Eplain. b. Wendy could not figure out the scale factor from Bug Wump to her new large Wump. What is this scale factor? (Hint: Applying the rule (,y) to Mug creates Bug.) 62

9 Additional Practice: Digital Assessments Investigation 2 5. The original figure below is transformed using the rule ( 2 1, 2y) y O Which of these points are vertices of the new transformed figure? Select all that apply. n (2, 0) n (2, 21) n (21, 2) n (2, 0) n (2, 21) n (1, 0) n (21, ) 6. Write the letter for each pair of figures in the correct bo. A Similar Figures C B D Not Similar Figures 6

10 Skill: Similar Figures Investigation 2 Tell whether the triangles are similar List the pairs of figures that appear to be similar. a. b. c. d. e. f. g. h. 6

11 Skill: Similar Figures (continued) Investigation 2 For Eercises 5 and 6, graph quadrilateral ABCD. Then graph its image A B C D with the given scale factor. 5. A(2, 2), B(, 2), C(, 2), D( 2, 2); scale factor 2 6 y O A(6, ), B(0, 6), C( 6, 2), D( 6, 5); scale factor 1 2 y O

12 Skill: Similar Figures (continued) Investigation 2 7. Quadrilateral A B C D is similar to quadrilateral ABCD. Find the scale factor from ABCD to A B C D. y 6 B 2 B C C A A 6 2 O D 6 D 66

13 Additional Practice Investigation 1. On the grid below, make a right triangle with legs of length 8 and 12. a. Give the leg lengths of two smaller right triangles that are similar to the one you drew and that have whole-number side lengths. b. Copies of each smaller triangle can be put together to eactly match the original triangle. How many of each smaller triangle does it take to match the original? 67

14 Additional Practice (continued) Investigation 2. In the grid below, each unit represents 1 centimeter. On the grid, make an isosceles triangle with base and height both equal to 6 centimeters. a. Can isosceles triangles with base and height equal to 2 centimeters be put together to eactly match the shape of the original triangle? Is each smaller triangle similar to the original? b. Can isosceles triangles with base and height equal to centimeters be put together to eactly match the shape of the original triangle? Is each smaller triangle similar to the original? 68

15 Additional Practice (continued) Investigation. Find the missing side lengths in each pair of similar figures below. a. cm 2 cm 8 cm b. 2 cm 2 cm cm cm 6 cm. For each pair of similar figures below, give the scale factor from figure A to figure B. a. b. B c. A A B B A 69

16 Additional Practice (continued) Investigation 5. a. The drawing below shows how a square foot and a square yard compare. How many square feet are in a square yard? Eplain your reasoning. 1 yd 1 ft 1 ft 1 yd b. Are a square foot and a square yard similar? If so, what is the scale factor from a square foot to a square yard? What is the scale factor from a square yard to a square foot? c. Compare a square inch with a square foot. What is the scale factor from a square inch to a square foot? d. How many square inches are in a square foot? Eplain. e. Compare a square inch with a square yard. What is the scale factor from a square inch to a square yard? f. How many square inches are in a square yard? 70

17 Additional Practice: Digital Assessments Investigation 1 6. The figures below are similar. Use the values in the bank to label the missing side lengths. 7. The two pentagons below are similar. Complete the missing side lengths using the values in the bank in. 2 in. in. 1 in. 2 in. in. in. 5 1 in. 2 in. in in. 0 2 in. 1 in. 8. Triangle ABC is similar to triangle A9B9C9. Circle the numbers that make the statements true. C C y A A O 1 2 B B The scale factor from triangle ABC to 2 Q triangle A9B9C9 is 1 U 2 because the coordinates of 1 2 each verte are multiplied by Q 1 U Rectangle A is a transformation of rectangle B, scaled by a factor of. How many copies of rectangle B can fit inside rectangle A? ~ 2 ~ ~ 8 ~ 16 71

18 Skill: Similar Polygons Investigation The pairs of figures below are similar. Find the value of each variable y y

19 Skill: Fractions, Decimals, and Percents Investigation Write three equivalent fractions for each fraction Write each fraction as a decimal and as a percent

20 Additional Practice Investigation 1. a. Rachel was working with the triangles below: cm 8 cm 2 cm 1 2 cm She wrote the fraction. What was she thinking about? 1 b. Net, she wrote the fraction while working with these two triangles: 18 cm 9 cm cm 6 cm Was she thinking in the same way or differently? Eplain. 7

21 Additional Practice (continued) Investigation 2. Below are several pairs of similar figures. In each, find the missing measurement(s). a. cm 7.5 cm cm a b. c 2.5 cm b 5 cm 1.5 cm c.. cm 2.5 cm 5 cm 6.95 cm 10 cm d e 75

22 Additional Practice (continued) Investigation. In each figure below, find the missing measurement. a. 2. cm cm 5 cm 1.8 cm b. y 6.72 cm 7 cm 25 cm 1.96 cm 76

23 Name Date Class Additional Practice: Digital Assessments Investigation. Using the values from the bank, find the missing measurement. 5. Which statements about the figures are true? Select all that apply. 5 cm 6 cm 10 cm 12 cm 18 cm cm 6 cm 2. cm D.2 cm C A 2.0 cm B 6.0 cm 1.2 cm E 1.0 cm H F 1.6 cm.0 cm G n ABCD is similar to EFGH. n Side AB is congruent to side EF. n Side DC corresponds to side HG. n The ratio of side AB to side AD is the same as the ratio of side EF to side EH. n The scale factor from ABCD to EFGH is Jaqué wants to calculate the scale factor for the pair of similar figures. Eplain how she can determine the scale factor from the figure on the left to the figure on the right. congruent First, she must identify the Q equivalent U corresponding sides. identical matching Because one side of length12 cm corresponds 12 cm 12 to a side of length Q 6 cm U, she divides 12 by Q 6 U. Q cm The result shows that the scale factor is 2 U cm cm 12 cm 6 cm 77

24 78 Investigation Name Date Class Skill: Similarity and Ratios Tell whether each pair of polygons is similar. Eplain why or why not P O R Q T S V U H I J G L M N K B A C 2 2 F D E T S U W X V J K L M I N O P Q R C B A D 12 8 H G E F 6

25 Skill: Similarity and Ratios (continued) Investigation Eercise 7 11 show pairs of similar polygons. Find the missing side lengths y y y 15 y y 15 79