IM 8 Ch 6.2.5 What Do SImilar Shapes Tell Us

1 IM 8 Ch what Do SImilar Shapes tell Us Common Core Standard: How do the Shapes grow or shrink? what parts can we compare? How can we write the comparison? CPM Materials modi ed by Mr. Deyo IM 8 Ch what Do SImilar Shapes tell Us Title: IM8 Ch. what Do SImilar Shapes tell Us? Date: Learning Target By the end of the period, I will apply scale factors to nd unknown side lengths. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity. IM 8 Ch what Do SImilar Shapes tell Us Home Work: Sec. Desc. Date Due Review & Preview 3 Problems: 6 92, 6 93, 6 97. IM 8 Ch what Do SImilar Shapes tell Us IM 8 Ch what Do SImilar Shapes tell Us Vocabulary 1) Transformation 2) Dilation 3) SImilar Figures 4) Congruent Figures IM 8 Ch what Do SImilar Shapes tell Us IM 8 Ch what Do SImilar Shapes tell Us what Do SImilar Shapes tell Us?

2 Graphic artists often need to make a shape larger to use for a sign. Sometimes they need to make a shape smaller to use for a bumper sticker. They have to be sure that the Shapes look the same no matter what size they are. How do artists know what the side length of a SImilar shape should be? That is, does it need to be larger or smaller than the original? As you work with your team with Shapes , ask the following questions: How can we use pairs of corresponding sides to write the scale factor? Will the scale factor between the Shapes be more or less than 1? Does it matter which pair of corresponding sides we use? IM 8 Ch what Do SImilar Shapes tell Us 6 86.

3 With your team, find the scale factor between each pair of SImilar Shapes . That is, what are the sides of each original shape multiplied by to get the new shape? a) scale factor: _____ b) scale factor: _____. IM 8 Ch what Do SImilar Shapes tell Us 6 87. It may have been easier to recognize the scale factor between the two Shapes in part (a) of problem 6 86 than it was to determine the scale factor between the two Shapes in part (b). When sides are not even multiples of each other (like the sides labeled 4 in. and 5 in. in part (b), it is useful to have another strategy for finding the scale factor. Your task: Work with your team to describe a strategy for finding the scale factor between any two Shapes .

4 Refer to the questions below to begin your discussion. Strategy for Finding the Scale Factor How can we use pairs of corresponding sides to write the scale factor? Will the scale factor between the Shapes be more or less than 1? Does it matter which pair of corresponding sides we use? IM 8 Ch what Do SImilar Shapes tell Us 6 88. A study team was working together to find the scale factor for the two SImilar triangles. Study Team 14 to find the Claudia set up the ratio scale factor. 4. 28 to find the Issac set up the ratio scale factor. 8. 21 to find the Paula set up the ratio scale factor. 6. a) what did the students do differently when they found their scale factors?

5 B) Do the triangles have more than one scale factor? If not, show how they are the same. c) Why does it make sense that the ratios are equal? IM 8 Ch what Do SImilar Shapes tell Us 6 89a. Alex was working with the two triangles from problem 6 86, but he now has a few more pieces of information about the sides. He has represented the new information and his scale factor in the diagram here. a) Use the scale factor to find the length of the side labeled x. Show your work. IM 8 Ch what Do SImilar Shapes tell Us 6 89b,c. Alex was working with the two triangles from problem 6 86, but he now has a few more pieces of information about the sides. He has represented the new information and his scale factor in the diagram here.

6 B) Since Alex multiplied the side lengths of triangle G to get triangle H, he needs to undo the enlargement to find the side labeled y. what math operation would he use to undo the enlargement? Write an expression and be prepared to explain your reasoning. (If you are able, simplify the expression to find y.). c) If triangle H had been the original triangle and triangle G had been the new triangle, how would the scale factor change? what would the new scale factor be? Explain IM 8 Ch what Do SImilar Shapes tell Us 6 90a. For the pairs of SImilar Shapes , find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair.

7 Assume the Shapes are all drawn to scale. x =. y =. IM 8 Ch what Do SImilar Shapes tell Us 6 90b. For the pairs of SImilar Shapes , find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the Shapes are all drawn to scale. x =. y =. IM 8 Ch what Do SImilar Shapes tell Us 6 90c. For the pairs of SImilar Shapes , find the lengths of the missing sides. Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the Shapes are all drawn to scale. x =. y =. z =. IM 8 Ch what Do SImilar Shapes tell Us 6 90d. For the pairs of SImilar Shapes , find the lengths of the missing sides.

8 Be sure to show your calculation. You can choose which shape is new and which is original in each pair. Assume the Shapes are all drawn to scale. x =. y =. z =. IM 8 Ch what Do SImilar Shapes tell Us 6 91. Additional Challenge: On graph paper, copy the figure shown. a) Find the area of the shape. b) Enlarge the shape by a scale factor of 2, and draw the new shape. Find the area. IM 8 Ch what Do SImilar Shapes tell Us homework/homework/category/CC/textbook/C C3/. 6 92. Find the scale factor and the missing side lengths. chapter/Ch6/ 92. x =. y =. IM 8 Ch what Do SImilar Shapes tell Us 6 93. Alex and Maria were trying to find the side labeled x in problem 6 92.

9 Their work is shown here. homework/homework/category/CC/textbook/C C3/. chapter/Ch6/ 93. Alex: "I noticed that when I multiplied Maria: "I remember that when we were dilating Shapes in Lesson , by 3, the sides of the triangle got longer.". my shape got bigger when I divided by 1 .". 3. a) Look at each student's work. Why do both multiplying by 3 and dividing by 1. make the triangles larger? 3. b) Use Alex and Maria's strategy to write two expressions to find the value of y in problem 6 92. IM 8 Ch what Do SImilar Shapes tell Us y = 3x 2. homework/homework/category/CC/textbook/C C3/. chapter/Ch6/ 94. 6 94a. Consider these two equations: y = 4 + 3x a) Graph both equations on the same set of axes.

10 Y = 3x 2 y = 4 + 3x x y x y IM 8 Ch what Do SImilar Shapes tell Us 6 94b,c. Consider these two equations: homework/homework/category/CC/textbook/C C3/. chapter/Ch6/ 94. b) Solve this system using the Equal Values Method. y = 3x 2 y = 4 + 3x c) Explain how the answer to part (b) agrees with the graph you made in part (a). IM 8 Ch what Do SImilar Shapes tell Us 6 95. Hollyhocks are tall, slender, flowering plants that grow in many areas of the Here are the heights (in inches) of hollyhocks that are growing in a park: homework/homework/category/CC/textbook/C C3/. chapter/Ch6/ 95. 10, 39, 43, 45, 46, 47, 48, 48, 49, 50, 52 a) Find the median. b) Find the quartiles.