Exploring Similar Figures

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1 Pre-Algebra Class Notes Name 6.3 Eploring Similar Figures (Day 1) Date Eploring Similar Figures Use the triangles below to answer the following questions. D 102 o A o 15 B 44 o 7 34 o C E 44 o o F 1. Which angle corresponds to A? 2. Which angle corresponds to B? 3. Which angle corresponds to C? 4. Does each angle and its corresponding angle have the same measurement, Yes or NO? 5. Which side corresponds to AB? 6. Which side corresponds to CB? 7. Which side corresponds to AC? 8. What is the ratio of side AB length to the length of it corresponding side? 9. What is the ratio of side BC length to the length of it corresponding side? 10. What is the ratio of side AC length to the length of it corresponding side? 11. What are the ratios equal to in lowest terms? 12. Are all three ratios equal, Yes or NO? 13. What is the scale factor of ABC to DEF?

2 Pre-Algebra Class Notes Section 6.3 Using Similar Figures (Day 2) Name Date Using Similar Figures Similar figures have two properties: The corresponding angles have measures. The lengths of corresponding sides are in. have the same shape, but not necessarily the same size. The symbol ~ means Write a proportion for corresponding sides.

3 Eit Slip 1. Given quadrilateral PQRS ~ TUVW, write a proportion to find the length of PS. 2. Given IJK ~ LMN, Find the length of IJ and then the length of IK. P S 35 Q R V 20 U 25 W J M T I 54 L y N K

compute distances that are difficult to measure directly. Such a process is called.

4 Pre-Algebra Class Notes Section 6.3 Using Indirect Measurement (Day 3) Name Date Indirect Measurement You can use similar figures to compute distances that are difficult to measure directly. Such a process is called. We will be using similar triangles to find the missing information. Draw a picture: Show your work: 1. Corresponding sides of similar triangles: 2. Write cross-products: 3. Simplify: Conclusion:

5 Use similar triangles to find the missing information (draw a picture for each problem). 1. If a 36-inch yardstick casts a 21-foot shadow, how tall is a building whose shadow is 168 feet? Show your work: Draw a picture: 4. Sam wants to enlarge a triangle with sides 3, 6 and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be? 2. Sam wants to enlarge a triangle with sides 3, 6 and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be? Show your work: Draw a picture:

Pre-Algebra Class Notes Section 6.3 Using Scale Drawings (Day 4) Using Scale Drawings Name Date A is an enlarged or reduced drawing that is similar to an actual object or place.

6 Pre-Algebra Class Notes Section 6.3 Using Scale Drawings (Day 4) Using Scale Drawings Name Date A is an enlarged or reduced drawing that is similar to an actual object or place. The ratio of a distance in the drawing to the corresponding actual distance is the scale of the drawing. 1. The distance from Sacramento to San Diego is about 480 mi. On a map whose scale is the same as the scale in the eample above. What is the approimate map distance between these two cities? Show your work: 1. Write a proportion: 2. Write cross-products: 3. Simplify: Conclusion:

2. The scale of the map is 1 in. : 44mi. About how far from Sacramento is Santa Rosa? Show your work: 1. Measure the map distance: 2. Write a proportion: 3. Write cross products: 4.

7 2. The scale of the map is 1 in. : 44mi. About how far from Sacramento is Santa Rosa? Show your work: 1. Measure the map distance: 2. Write a proportion: 3. Write cross products: 4. Simplify: Conclusion: 3. The distance from Sacramento to San Jose is about 121 mi. What is the approimate map distance between these two cities? (Use the image on problem 2). Show your work:

8 -1- Y b250u1h3x ckuurtcan 7SEoffJtLwLaZrte3 dlhl0c0.3 n kaol1ln draiugmh6tbse BrDeJsveIrqvLed5.9 4 kmpaadqen kwhiltchh wionjfki6nvibtte8 yparuez-dael6gne1bjrha8.9 Worksheet by Kuta Software LLC Pre-Algebra -Assignment #20 DUE: 3/26/13 Secton 6.3 Eploring Similar Figures (Day 1) j t2p01d3q OKou4taa0 3Sko1fBtnwNa2rlec MLDLTC.r 1 iaaldls ZrGiHgThqtLso Qr8eIsGeNr4vpe6d4.H Each pair of figures is similar. Find the missing side. Name Date 1) 2) ) 4) ) 6)

9 -2- O 32D0y1j3D IKnugtoaK NSDoYfetowfaZrQei il1l9ct.o L RAKlFl8 UrMiigHh5tIs9 zroebsseorrvmesdw.o W cmfawdfeo fweijtvh8 zicn7fhien8i6t0ec ppzr9em-talliglehbrreas.c Worksheet by Kuta Software LLC 7) ) ) ) ) )

10 Pre-Algebra Homework #21 (DUE: 3/27/13) Section 6.3 Using Similar Figures (Day 2) Name Date Find the missing side lengths in each pair of similar figures. 1. ABC ~ XYZ 2. ABC ~ XYZ A 25 X 6 Z 8 10 Y A 50 Y 20 Z X C B C 40 B 3. ABC ~ XYZ 4. ABC ~ XYZ A Y 15 Z A 5 Z y 14.4 Y X B C 30 B C y X 5. JKL ~ GKH 6. ABC ~ ADE K D G 4 H y B 3 5 J 15 L A 4 C E

11 Pre-Algebra Homework #22 (DUE: 3/28/13) Section 6.3 Using Indirect Measure (Day 3) Name Date Use similar triangles to find the missing information. 1. A giraffe is 18 feet tall and casts a shadow of 12 feet. Corry casts a shadow of 4 feet. How tall is Corry? 2. When a Ferris wheel casts a 20-meter shadow, a man 1.8 meters tall casts a 2.4-meter shadow. How tall is the Ferris wheel? 3. A flagpole casts a shadow 28 feet long. A person standing nearby casts a shadow eight feet long. If the person is si feet tall, how tall is the flagpole?

12 4. A photograph measuring four inches wide and five inches long is enlarged to make a wall mural. If the mural is 120 inches wide, how long is the mural? 5. A 9-foot ladder leans against a building si feet above the ground. At what height would a 15-foot ladder touch the building if both ladders form the same angle with the ground? 6. Chris wants to reduce a triangular pattern with sides 16, 16 and 20 centimeters. If the longest side of the new pattern is to be 15 cm, how long should the other two sides be?

13 -1- k A210a1c3g BKMu7twa3 JS3otf1tqwGakreV dlgldc4.o T baalel5 brnidgfhqt9st brhemsgezr2vtebdt.r o HM8addheK 0wiiAtchh sivnvfdivn3ihtgej lpcreei-amlyghejbdr8au.q Worksheet by Kuta Software LLC Pre-Algebra Homework #23 DUE: 4/8/13 Name Section 6.3 Using Scale Drawings (Day 4) D f2y0q1n3k QKHu9tyaE cs6obfct5wuayrnee qlhljcb.k V PA9lllN mrci7g2h5tmsn hr9edsretrxvteadi.9 Answer each question and round your answer to the nearest whole number. Date 1) A model giraffe has a scale of 3 in : 2 ft. If the real giraffe is 14 ft tall then how tall is the model giraffe? 2) A model car is 12 in long. If it was built with a scale of 2 in : 3 ft then how long is the real car? 3) A particular statue is 10 ft wide. A model of it was built with a scale of 5 in : 2 ft. How wide is the model? 4) A model satellite has a scale of 2 in : 5 yd. If the real satellite is 20 yd wide then how wide is the model satellite? 5) A model car has a scale of 3 in : 5 ft. If the real car is 15 ft long then how long is the model car? 6) A model rocket has a scale of 2 cm : 1 m. If the real rocket is 14 m tall then how tall is the model rocket?

14 -2-4 2T0G1k36 3KauHtIae psxo0fatiwiafrke0 slwlacr.i y TABlOlK proiwgvh3tdsi 5rXeesWedr3vmejd4.f G PM6aRdDeA tw1iwtvhn 8I4nOfHiFnmiUtEet op5rueo-qa0lvgqegborcap.s Worksheet by Kuta Software LLC 7) A model train has a scale of 4 in : 3 ft. If the real train is 9 ft tall then how tall is the model train? 8) A model train has a scale of 3 in : 2 ft. If the model train is 24 in tall then how tall is the real train? 9) A model statue is 36 in tall. If it was built with a scale of 4 in : 2 ft then how tall is the real statue? 10) A model rocket has a scale of 4 cm : 2 m. If the model rocket is 32 cm tall then how tall is the real rocket?

15 Name Class Date Reteaching 6-3 Similar Figures and Scale Drawings Similar triangles have the same shape but not necessarily the same size. In the figures, n ABC is similar to n DEF. The symbol, means is similar to. n ABC,nDEF. The lengths of the sides of similar triangles are always proportional to each other. Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Find EF. Substitute into Write a proportion. Find the cross products. Divide each side by 8. Simplify. Use the properties of similar triangles to calculate the side lengths in each problem. 1. n MNP,nSTW. a. Complete: ; b. Substitute the correct lengths in the above proportions and solve SW n DKL,nREV. DK 5 RV 5 3. n ANF,nKGS. AN 5 GS 5 SW 5 AC DF 5 EF BC ; MN ST 5 MP SW 27 NP 24 NP MN ST 5 TW NP 5 D A N K B A 6 8 M N 36 L R 44 F C E 18 G K E S P 3 15 D 60 T 48 4 F 24 V S W Reteaching Pre-Algebra Lesson

16 Name Class Date Puzzle 6-3 Similar Figures and Scale Drawing Use what you know about proportions and similar figures to calculate the length of the missing side in each pair of similar figures. The missing digits will tell the year that the first mathematics books were printed. A B C D Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved ? ? ? 9 36 A B C D 12? The first mathematics books were published in the year. Puzzle Pre-Algebra Lesson

17 Name Class Date Practice 6-3 Similar Figures and Scale Drawings 1 The scale of a map is 2 in. : 8 mi. Find the actual distance for each map distance in in. 3. in. 32 mi in in. 6. in. 160 mi 80 mi 128 mi mi 116 mi Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Each pair of figures is similar. Find the missing length. Round to the nearest tenth where necessary n n A meter stick casts a shadow 1.4 m long at the same time a flagpole casts a shadow 7.7 m long. The triangle formed by the meterstick and its shadow is similar to the triangle formed by the flagpole and its shadow. How tall is the flagpole? m 1 p A scale drawing has a scale of 4 in. : 6 ft. Find the length on the drawing for each actual length ft ft ft e < 21 p e 6 17 f f < in in. in Practice Pre-Algebra Lesson

Similar Figures 2.5. ACTIVITY: Reducing Photographs. How can you use proportions to help make decisions in art, design, and magazine layouts?

Similar Figures 2.5. ACTIVITY: Reducing Photographs. How can you use proportions to help make decisions in art, design, and magazine layouts? .5 Similar Figures How can you use proportions to help make decisions in art, design, and magazine layouts? In a computer art program, when you click and drag on a side of a photograph, you distort it.