Understanding Similar Figures and Scale Drawings in Geometry

© 2018 The Algebros, LLC Write your questions here! 13.1 Similar Figures Similar - CORRESPONDING ANGLES CORRESPONDING SIDES ∠𝐿𝐿 corresponds to _____ 𝑀𝑀𝑀𝑀 �� corresponds to _____ ∠ 𝑂𝑂 corresponds to _____ 𝑀𝑀𝐴𝐴 �� corresponds to _____ ∠ 𝑉𝑉 corresponds to _____ 𝐴𝐴𝑇𝑇 �� corresponds to _____ ∠ 𝐸𝐸 corresponds to _____ 𝑇𝑇𝑀𝑀 �� corresponds to _____ NOTES

© 2018 The Algebros, LLC SUMMARY: 13.1 Similar Figures The following figures are similar. Fill in the blanks. 1. 𝑀𝑀𝐴𝐴𝐴𝐴𝐴𝐴 ~ _______ a. ∠𝐿𝐿 corresponds to _____ b. 𝐴𝐴𝐴𝐴 �� corresponds to _____ c. ∠𝐴𝐴 corresponds to _____ d. 𝑁𝑁𝑀𝑀 �� corresponds to _____ 2. 𝑀𝑀𝑁𝑁𝐴𝐴 ~ _____ a. ∠𝑁𝑁 corresponds to _____ b. 𝑁𝑁𝑀𝑀 �� corresponds to _____ c. ∠𝑌𝑌 corresponds to _____ d. 𝐹𝐹𝑌𝑌 �� corresponds to _____ PRACTICE Now, summarize your notes here!

© 2018 The Algebros, LLC The following figures are similar. State the scale factor, set up a proportion, and find the missing side. 3. Scale Factor = 4. Scale Factor = 5. Scale Factor = 6. Scale Factor = 7. Scale Factor = 8. Scale Factor =

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© 2018 The Algebros, LLC 13.1 Similar Figures Use the similar figures shown below to answer 1-4. 1. ∠𝐴𝐴 corresponds to _____ 2. 𝐴𝐴𝐷𝐷 �� corresponds to _____ 3. What is the scale factor? 4. Find the length of 𝐴𝐴𝐴𝐴 . 𝑪𝑪𝑪𝑪𝑪𝑪 ~ 𝑫𝑫𝑫𝑫𝑫𝑫 5. A 32 foot tree casts a 60 foot shadow as shown below. A man next to the tree casts a 12 foot shadow. How tall is the man? Justify your solution. EXIT TICKET – WRAP UP The scale factor of the similar figures below is 5:2. Given 𝐴𝐴𝐸𝐸 = 10 feet , find the length of 𝑀𝑀𝐴𝐴 . 𝐾𝐾𝐾𝐾𝐴𝐴𝐸𝐸 ~ 𝑄𝑄𝑄𝑄𝑀𝑀𝐴𝐴

© 2018 The Algebros, LLC Write your questions here! 13.2 Scale Drawings Original Triangle Scale Factor = 2 Scale Factor = 1 3 Scale Factor = 7 4 MODELS Below is a replica of 1/18 scale 1958 Chevrolet Corvette diecast model. Diecast model car 1:18. If the real convertible is 63 inches wide, how wide is the model? MAPS If it is 2.5 cm on the map from Beijing to Shanghai, how far is that in real life? NOTES

© 2018 The Algebros, LLC DRAWINGS 1 unit = 5 feet What are the dimensions of the real living room? Add a room off the living room that is 15’ by 18.5’. SUMMARY: 13.2 Scale Drawings Label the sides of the similar figures with the given scale factor. 1. Original Triangle Scale Factor = 3 4 Scale Factor = 3 2 2. Original Triangle Scale Factor = 5 2 Scale Factor = 1 4 PRACTICE Now, summarize your notes here!

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© 2018 The Algebros, LLC Use proportions to solve the following. 3. Hot Wheels are designed to be 1:64 of the real automobile. Mr. Brust wants to make a Hot Wheel made of his Toyota Sienna Minivan. If the width of Mr. Brust’s minivan is 200 cm. How wide would his minivan Hot Wheel be? 4. An architect makes a model of house with a pool. 1.5 cm of the model is equal to 3 meters in real life. If the model pool is 3.2 cm long, how long is the real pool? 5. Mr. Brust wants to drive from Dayton to Cincinnati. The map has a scale of 2 cm = 15 miles. If Mr. Brust measure the distance between the two cities as 7 cm. How far apart are the cities? 6. The scale of a map is ½ inch equals 28 miles. If two cities are 460 miles away in real life, how far apart will they be drawn on the map? 7. Mr. Brust drew the picture of a flea below. The ratio of drawing to real flea is 80:1. How long is a real flea?

© 2018 The Algebros, LLC 8. The scale is 2 units = 15 feet. What are the real-life dimensions of the family room? 9. The scale is 1 unit = 7 feet. Draw a scaled version of a 42 foot by 24.5 foot rectangular kitchen. 10. Amazon is selling a model of the F/A-18 Hornet series fighter aircraft. The description is shown next to the model. Model Description: Skill Level: 2 Scale: 1/48 Length: 15" Wingspan: 11" Parts: 110+ a. What is the length of a real Hornet fighter aircraft? SHOW WORK! b. What is the wingspan of a real Hornet fighter aircraft? SHOW WORK! Family Room

© 2018 The Algebros, LLC 13.2 Scale Drawings Use proportions to solve the following. 1. A GI Joe figure is 2:45 of the real person. If the figure is 8.25 cm, how tall is the real person? 2. The key on a map says that 3 cm = 120 km. How far on the map would 1500 km be? 3. Make a scale drawing of the following. Include your scale factor! EXIT TICKET – WRAP UP Mr. Sullivan wants to make a mural on the wall of his face. He plans to enlarge his face by a factor of 8 1 2 . Is the wall below big enough for his head? Justify your solution.

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© 2018 The Algebros, LLC Write your questions here! 13.3 Area and Perimeter Original Rectangle Scale Factor = 2 Original Perimeter = Original Area = New Perimeter = New Area = The ratio of original perimeter to similar perimeter is______ The ratio of original area to similar area is _________ A rectangle with perimeter of 30 cm is scaled up by a factor of 3. What is the new rectangle’s perimeter? A rectangle with area of 20 cm 2 is scaled up by a factor of 3. What is the new rectangle’s area? Find the perimeter and area. Original Triangle Original Area = Scale Factor = 1 4 New Area = SUMMARY: NOTES Now, summarize your notes here!

© 2018 The Algebros, LLC 13.3 Area and Perimeter Find the area of the following. Label you answer! 1. 2. 3. Draw and label the sides of the similar figures with the given scale factor. Find the perimeter and area. 4. Original Figure Original Perimeter = Original Area = Scale Factor = 3 New Perimeter = New Area = How many times bigger is the new area to the original area? 5. Original Figure Original Perimeter = Original Area = Scale Factor = 2 New Perimeter = New Area = PRACTICE How many times bigger is the new perimeter to the original perimeter? m

© 2018 The Algebros, LLC Label the sides of the similar figures with the given scale factor. Find the perimeter and area. 6. Original Figure Original Perimeter = Original Area = Scale Factor = 1 2 New Perimeter = New Area = 7. Original Figure Original Perimeter = Original Area = Scale Factor = 4 New Perimeter = New Area = Answer the following. 8. A rectangle with perimeter of 120 cm is scaled up by a factor of 5. What is the new rectangle’s perimeter? 9. A rectangle with area of 40 cm 2 is scaled up by a factor of 5. What is the new rectangle’s area? 10. A triangle with perimeter of 28 ft is scaled down by a factor of 3 4 . What is the new rectangle’s perimeter? 11. A triangle with area of 54 cm 2 is scaled down by a factor of 1 3 . What is the new rectangle’s area? How many times bigger is the new perimeter to the original perimeter? How many times bigger is the new area to the original area?

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© 2018 The Algebros, LLC 13.3 Area and Perimeter 1. Find the area. 2. A rectangle with area of 24 cm 2 is scaled up by a factor of 4. What is the new rectangle’s area? 3. Given 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 ~ 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 and the area of figure 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 = 36 𝑚𝑚 2 , find the area of figure 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 . EXIT TICKET – WRAP UP Sully is tiling his kitchen below. Tile cost $3.50 per square foot. Mr. Kelly is tiling his kitchen with the same tiles. The dimensions of Kelly’s kitchen are twice as big as Sully’s kitchen. Mr. Kelly thinks that he will spend twice as much as Sully. Is correct? Justify your solution.

Unit 13 Similarity NAME:__________________________ DATE:_______ The following figures are similar. Fill in the blanks and answer the questions. 1. 𝐶𝐶𝐶𝐶𝐶𝐶 ~ _______ a. Find 𝑥𝑥 . b. 𝐶𝐶𝐶𝐶 �� corresponds to _____ c. ∠𝐷𝐷 corresponds to _____ d. What is the scale factor? 2. 𝐺𝐺𝐺𝐺𝐺𝐺𝐶𝐶 ~ _______ a. 𝐺𝐺𝐶𝐶 �� corresponds to _____ b. ∠𝐶𝐶 corresponds to _____ c. 𝑊𝑊𝑊𝑊 𝐴𝐴𝐴𝐴 = 𝐺𝐺𝑊𝑊 𝐹𝐹𝐴𝐴 is true or false? d. What is the scale factor? e. Find the length of 𝐺𝐺𝐺𝐺 . f. Find the length of F 𝐻𝐻 . 3. The scale is 2 units = 13 feet. a. What are the real-life dimensions of the family room? b. What is the area of the real family room? Review Family Room

Draw and label the sides of the similar figures with the given scale factor. Find the perimeter and area. 4. Original Figure Original Perimeter = Original Area = Scale Factor = 2 New Perimeter = New Area = How many times bigger is the new perimeter to the original perimeter? How many times bigger is the new area to the original area? Use proportions to solve the following. 5. The scale on a map is 1.5 cm equals 40 km in real life. You measure the distance between two cities on the map as 14 cm. How far apart are the cities in real life? 6. A baby doll is 1:12 of a real baby. If the real baby is 14 inches long, how big is the doll? 7. Mr. Kelly buys a wallet size portrait of himself. He wants a poster made of his face from the wallet size that would be at the ratio 15:2. What are the dimensions of the poster?

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