UNIT 3 STRECHING AND SHRINKING ASSIGNMENTS NAME

UNIT 3 STRECHING AND SHRINKING ASSIGNMENTS NAME

Day 1 (1.1 Investigation) For exercises 1 and 2, use the drawing at the right, which shows a person standing next to a ranger s outlook tower. 1. Find the approximate height of the tower if the person is a. 6 feet tall b. 5 feet 6 inches tall 2. Find the approximate height of the person if the tower is a. 28 feet tall b. 36 feet tall 3. Suppose you copy a drawing of a polygon using the given size factor. How will the side lengths, angle measures, and perimeter of the image compare to those of the original? a. 200% b. 50% For exercises #4 and #5, find the perimeter and the area of each figure. SHOW WORK. 4. 5. 5. Find the given percent of each number. Show your work. a. 25% of 120 b. 120% of 80 For #6 and #7, circle the correct answer. 6. What is the 5% sales tax on a $14.00 compact disc? a. $0.07 b. $0.70 c. $7.00 d. $70.00 7. What is the 15% service tip on a $25.50 dinner in a restaurant? a. $1.70 b. $3.83 c. $5.10 d. $38.25

EXTENSION 8. A movie projector that is 6 feet away from a large screen shows a rectangular picture that is 3 feet wide and 2 feet high. a. Suppose the projector is moved to a point 12 feet from the screen. What size will the picture be (width, height, and area)? b. Suppose the projector is moved to a point 9 feet from the screen. What size will the picture be (width, height, and area)? SPIRAL 9. If measure of angle 3 in this diagram is 55, 11. Find the measure of each angle. find the measures of: angle 2: angle 7: Day 2 (2.2 Investigation) 1. On grid, draw triangle ABC with vertex coordinates A(0, 2), B(6, 2), C(4, 4). a. Apply the rule (1.5x, 1.5y) to the vertices of triangle ABC to get triangle PQR. Draw the new triangle. Coordinates of the new triangle: P (, ) Q(, ) R(, ) How do the following features of the new triangle compare to the original one? Side lengths: Perimeters: Areas: Angle measures:

b. Apply the rule (2x, 0.5y) to the vertices of triangle ABC to get triangle FGH. Draw the new triangle. Coordinates of the new triangle: F (, ) G(, ) H(, ) How do the following features of the new triangle compare to the original one? Side lengths: Perimeters: Areas: Angle measures: c. Which triangle, PQR or FGH, seems similar to triangle ABC? Explain why? 2. On grid, draw parallelogram ABCD with vertex coordinates A(0, 2), B(6, 2), C(8, 6), D(2, 6). a. Write a rule to find the vertex coordinates of a parallelogram PQRS that is larger than but similar to ABCD. Test your rule to see if it works. Rule: P (. ) Q(. ) R(. ) S(. ) b. Write a rule to find the vertex coordinates of a parallelogram TUVW that is smaller than but similar to ABCD. Test your rule to see if it works. Rule: T (. ) U(. ) V(. ) W(. ) For exercises #3 and #4, what is the percent reduction or enlargement that will result if the rule is applied to a figure on a coordinate grid? 3. (1.5x, 1.5y) a. 150% b. 15% c. 1.5% d. None of these 4. (0.7x, 0.7y) a. 700% b. 7% c. 0.7% d. None of these

EXTENSION (instead of #2) 5. The vertices of three similar triangles are given. Triangle ABC: A(1, 2), B(4, 3), C(2, 5) Triangle DEF: D(3, 6), E(12, 9), F(6, 15) Triangle GHI: G(5, 9), H(14, 12), I(8, 18) a. Find a rule that changes the vertices of triangle ABC to the vertices of triangle DEF. b. Find a rule that changes the vertices of triangle DEF to the vertices of triangle GHI. c. Find a rule that changes the vertices of triangle ABC to the vertices of triangle GHI. SPIRAL 6. The measure of one angle is 73. a. Find the measure of its complement? b. Find the measure of its supplement? Day 3A (2.3 Investigation) For exercises #1 and #2, study the size and shape of the polygons below. 1. Choose the pair of similar figures. a. Z and Y b. V and T c. X and Y d. Y and W 2. Find another pair of similar figures. Explain your reasoning.

3. An accurate map is a scale drawing of the place it represents. Below is a map of South Africa. a. Use the scale to estimate the distance from Cape Town to Port Elizabeth. b. Use the scale to estimate the distance from Johannesburg to Cap Town. c. What is the relationship between the scale for the map and a scale factor? SPIRAL In the drawing, name two angles that are complementary to each other. EXTENSION Solve for x: x (2x 30) (2x + 40) (3x 10)

Day #3B (2.3 Investigation) 1. The diagram on the right shows two similar polygons. a. Write a rule for finding the coordinates of a point on Figure B from the corresponding point on Figure A. b. Write a rule for finding the coordinates of a point on Figure A from the corresponding point on Figure B. c. What is the scale factor from Figure A to Figure B? d. What is the scale factor from Figure B to Figure A? 2. Use the polygons below to answer: a. Which pairs of polygons are similar figures? b. For each pair of similar figures, list corresponding sides and angles. c. For each pair of similar figures, find the scale factor that relates side lengths of the larger figure to the corresponding side lengths of the similar figure

EXTENSION 3. On grid paper, draw a rectangle with an area of 14 square centimeters. Label it ABCD. a. Write and use a coordinate rule that will make a rectangle similar to rectangle ABCD that is three times as long and three times as wide. Label it EFGH. b. How does the perimeter of rectangle EFGH compare to the perimeter of rectangle ABCD? c. How does the area of rectangle EFGH compare to the area of rectangle ABCD? d. How do your answers to parts (b) and (c) relate to the scale factor from rectangle ABCD to rectangle EFGH? Day #3C (Additional Practice 2.2-2.3) 1. On a coordinate paper, draw any rectangle that is not a square. Draw a similar rectangle by applying a scale factor of 3 to the original rectangle. (Measure precisely and use small measurements so the enlarged rectangle can fit as well) 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?

2. Make a figure by connecting the following sets of points on a coordinate grid: A (1, 1) B (5, 2) C (4, 4) a. Suppose you used the rule (2x,2y) to transform this figure into a new triangle DEF. How would the angles of the new figure compare with the angles of the original? b. How would the side lengths DEF compare to the side lengths of the original ABC? c. Would the new figure DEF be similar to the original ABC? Explain your reasoning. d. Suppose you used the rule (2x + 1, 2y 4) to transform the original figure into a new figure HGI. How would the angles of the new figure HGI compare with the angles of the original ABC? e. How would the side lengths of the new figure HGI compare to the side lengths of the original ABC? f. Would the new figure HGI be similar to the original ABC? Explain your reasoning. 3. A copy was made from an original picture using a scale factor of 3. What is the scale factor from the copy to the original picture? Explain. 4. Wendy drew a very large copy of a heart using the rule (8x,8y). She said that the scale factor from her drawing to the original heart was 8. a. Do you agree with Wendy? Explain. b. Wendy could not figure out the scale factor from her drawing to the original heart. What is this scale factor?

Day 4 (3.1-3.2 Investigation) 1. Look for rep-tile patterns in the designs below. Design A Design B a. For each design, give the scale factor from each small quadrilateral to the large quadrilateral. Design A Design B b. How is the area of the larger rectangle related to the area of the smaller rectangle? Design A Design B 2. Suppose you divide a rectangle into 25 smaller rectangles such that each rectangle is similar to the original rectangle. a. How is the area of each of the smaller rectangles related to the area of the original rectangle? b. What is the scale factor from the original rectangle to each of the smaller rectangles? 3. Look for rep-tile patterns in the figures below. Tell whether the small triangles are similar to the large triangle. Explain. If the triangles are similar, give the scale factor from each small triangle to the large triangle.

4. The right triangles are similar: a. Find the length of side RS. b. Find the length of side RQ. c. If the measure of angle x were exactly 40, what would be the measure of angle y? d. Use your answer from part (c) to find the measure of angle R. Explain how you can find the measure of angle C. e. Angle x and angle y are complementary angles. Find two additional pairs of complementary angles in the triangle QRS. For exercises #5 7, decide whether the statement is true or false. Explain your reasoning. 5. All squares are similar. 6. All rectangles are similar. 7. If the scale factor between two similar shapes is 1, then the two shapes are the same size. SPIRAL 8. In the figure below, lines L 1 and L 2 are parallel. a. Use what you know about parallel lines to find the measures of angles a through g. b. List all pairs of supplementary angles in the diagram. 9. For each of the following angle measures, find the measure of its supplementary angle. a. 160 b. 90 c. x

Day 5 (3.3 Investigation) Triangle ABC is similar to triangle PQR. For exercises #1 6, find the indicated angle measure or side length. SHOW WORK. 1. angle A 2. angle Q 3. angle P 4. length of side AB 5. length of side AC 6. perimeter of triangle ABC For problems #7-10, write both scale factors and then choose the appropriate one to find the missing lengths. Write scale factors in both fraction and decimal form. 7. 8. SF small to big: SF big to small: x = SF small to big: SF big to small: y = 9. 10. SF small to big: SF big to small: x = SF small to big: SF big to small: x = y =

11. Use the scale factor to find the height of the taller tree. SPIRAL 12. Would the given side lengths make up a triangle? Explain. a. 7, 12, 4 b. 13, 19, 7 EXTENSION (instead of #9 and #10) Write both scale factors and then choose the appropriate one to find the missing lengths. Write scale factors in both fraction and decimal form. D E SF TVF to EVC: SF EVC to EVF: x = SF ABE to ACD: SF ACD to ABE: h =

Day 6 (3.4 Investigation) 1. Judy lies on the ground 45 feet from her tent. Both the top of the tent and the top of a tall cliff are in her line of sight. Her tent is 10 feet tall. About how high is the cliff?. Assume the two triangles are similar. First, draw two separate triangles and label them. For exercises #2 and #3, each triangle has been subdivided into triangles that are similar to the original triangle. Label the separate triangles and find the missing side lengths. 2. 3. 4. Use the rectangle to answer the questions. a. Suppose the following rectangle is reduced by a scale factor of 50%.What are the dimensions of the reduced rectangle? b. Suppose the reduced rectangle from part (a) is reduced again by a scale factor of 50%. What are the dimensions of the new rectangle? Explain your reasoning. c. How does the reduced rectangle from part (b) compare to the original rectangle from part (a)? 5. What is the value of x? The diagram is not to scale. First, draw two separate triangles and label them. a. 3cm b. 10 cm c. 12 cm d. 90 cm

Day 7 (4.1 Investigation) 1. List all the pairs of similar parallelograms. Explain your reasoning. 2. Draw two similar rectangles where the scale factor from one rectangle to the other is 2.5. Label the length and width of each rectangle. For each rectangle, find the ratio of the length to the width. EXTENSION y Find the side length for both x and y. Show all of your work using the appropriate scale factor. 8 6 6 x 9

SPIRAL 3. Use a straightedge and a protractor to draw two different triangles that each has angle measures of 30, 60, and 90. Do the triangles appear to be similar? 4. If you drew two triangles that each has angle measures of 40, 80, 60, would the triangles appear to be similar? Explain your reasoning. Day 8 (4.2 Investigation) For exercises #1 3, each pair of figures is similar. Find the missing measurement. Explain your reasoning. (Note: The figures are not drawn to scale.) 1. 2. 3.

For #4 and 5, use the triangle below. The drawings are not to scale. 4. List all the pairs of similar triangles. Explain why they are similar. 5. For each pair of similar triangles above, find the scale factor from one shape to the other. Explain how the information given by the scale factors is different than the information given by the ratios of side lengths. 6. Rectangles C and D are similar. a. What is the value of x? b. What is the scale factor from rectangle C to rectangle D? SPIRAL 7. Would the given side lengths make up a triangle? Explain. a. 5, 5, 5 b. 11, 19, 6 8. Would the given angle measures make up a triangle? Explain. b. 37, 49, 102 b. 62, 63, 55

Day 9 (4.3 Investigation) 1. The pair of triangles below is similar. Find the missing measurement. Explain your reasoning. (Note: The figures are not drawn to scale.) 2. Movie screens often have an aspect ratio of 16 by 9. This means that for every 16 feet of width along the base of the screen there are 9 feet of height. The width of the screen at a local drive-in theater is about 115 feet wide. The screen has a 16:9 aspect ratio. About how tall is the screen? 3. Triangle A has sides that measure 4 inches, 5 inches, and 6 inches. Triangle B has sides that measure 8 feet, 10 feet, and 12 feet. Taylor and Landon are discussing whether the two triangles are similar. Do you agree with Taylor or with Landon? Explain. 4. Tell whether each pair of ratios is equivalent. a. 3 to 2 and 5 to 4 b. 7 to 5 and 21 to 15 5. Paloma draws triangle ABC on a grid. She applies a rule to make the triangle on the right. a. What rule did Paloma apply to make the new triangle? b. Is the new triangle similar to triangle ABC? Explain your reasoning. If the triangles are similar, give the scale factor from triangle ABC to the new triangle.

EXTENSION Suppose a photographer for the school newspaper took this picture. The editors want to resize the photo to fit in a specific space on a page. (4 inches by 6 inches) 6. Can the original photo be changed to a similar rectangle with the given measurements (in inches)? a. 8 by 12 b. 9 by 11 c. 6 by 9 d. 3 by 4.5 7. Suppose that the school copier only has three paper sizes (in inches): 8½ by 11, 11 by 14, and 11 by 17. You can enlarge or reduce documents by specifying a percent from 50% to 200%. Can you make copies of the photo that fit exactly on any of the three paper sizes? Explain your reasoning. 8. What is the greatest enlargement of the photo that fit on the paper that is 11 inches by 17 inches? Day 10 (4.4 Investigation) 1. The Washington Monument is the tallest structure in Washington, D.C. At a certain time, the monument casts a shadow that is about 500 feet long. At the same time, a 40-foot flagpole nearby casts a shadow that is about 36 feet long. About how tall is the monument? Sketch a diagram.

2. Darius uses the shadow method to estimate the height of a flagpole. He finds that a 5-foot stick casts a 4-foot shadow. At the same time, he finds that the flagpole casts a 20-foot shadow. What is the height of the flagpole? Sketch a diagram. 3. The Rosavilla School District wants to build a new middle school building. They ask architect to make scale drawings of possible layouts for the building. Two possibilities are shown. The school board likes the L-shaped layout but wants a building with more space. They increase the L- shaped layout by a scale factor of 2. For the new layout, choose the correct statement. A. The area is two times the original. B. The area is four times the original. C. The area is eight times the original. D. None of the statements above are correct. 4. The school principal visits Ashton s class one day. Ashton uses the mirror method to estimate the principal s height. This diagram shows the measurements he recorded. a. What estimate should Ashton give for the principal s height? b. Is your answer in part (a) a reasonable height for an adult? 5. The rectangles in the drawing are similar. a. What is the scale factor from Rectangle A to Rectangle B? b. What is the value of x? Explain your reasoning. c. What is the ratio of the area of Rectangle A to the area of Rectangle B?

Choose ONE of the three problems below to solve. 6. Greg and Zola are trying to find the height of their school building. Zola takes a picture of Greg standing next to the building. a. How might this picture help them determine the height of the building? b. Greg is 5 feet tall. The picture Zola took shows Greg as ¼ inch tall. If the building is 25 feet tall in real life, how tall should the building be in the picture? Explain. c. In part (a), you thought of ways to use a picture to find the height of an object. Think of an object in your school that is difficult to measure directly, such as a high wall, bookshelf, or trophy case. Describe how you might find the height of the object. 7. Francisco, Katya, and Peter notice that all squares are similar. They wander if other shapes that have four sides are all-similar. Who is correct? Explain. 8. Ernie and Vernon are having a discussion about all-similar shapes. Ernie says that regular polygons and circles are the only types of all-similar shapes. Vernon claims isosceles right triangles are all-similar, but they are not regular polygons? Who is correct? Explain.

EXTENSION SPIRAL Find the value of x in the figure. Then find the size of the angles. 1. 2. (x + 2) 3. (2x + 40) 140 (3x 2) (3x + 60) (7x 80) Find the value of x that makes lines m and n parallel. 4. 5. m 2x (6x + 10) 8x t n (6x 20) m n t