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Name7-1ClassDateELL SupportRatios and ProportionsComplete the vocabulary chart by filling in the missing information.Word orWord PhraseDescriptionPicture or ExampleratioA ratio is a comparison of twoquantities by division.2 to 9, 2 i 9, or 29proportion1. A proportion is an equation thatstates that two ratios are equal.3221 5 14extremes2. The extremes are the first and lastnumbers in a proportion.3221 5 14meansThe means are the middle twonumbers in a proportion.3. 3221 5 14extended ratio4. An extended ratio compares threeor more numbers.An isosceles right trianglehas angle measures thatare in the extended ratio45 i 45 i 90.Cross ProductsPropertryIn a proportion, the product of theextremes equals the product of themeans.5.32125 143 ? 14 5 2 ? 2142 5 42Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.1
Name7-1ClassDateThink About a PlanRatios and ProportionsReasoning The means of a proportion are 4 and 15. List all possible pairs ofpositive integers that could be the extremes of the proportion.Understanding the Problem1. What is a proportion? an equation that states two ratios are equal2. What are some of the forms in which a proportion can be written?Answers may vary. Samples: a i b 5 c i d or ba 5 dc3. Explain the difference between the means and the extremes of a proportion.Use an example in your explanation.When you write a proportion in the form a i b 5 c i d, the first and last numbers arethe extremes and the middle numbers are the means. In this example a and d are theextremes and b and c are the means.Planning the Solution4. How can you write the proportion described in the problem, using variablesfor the extremes? Should you use the same variable for the extremes ordifferent variables?a i 4 5 15 i b; use different variables because the extremes may be different numbers.5. How can you rewrite the proportion as equivalent fractions?a45 15b6. How do you solve for variables in a proportion? Apply this to the proportionyou wrote in Step 5. Find the cross-products; ab 5 60.Getting an Answer7. Look at the equation you wrote in Step 6. How do the two variables on the oneside of the equation relate to the value on the other side?The value is the product of the two variables.8. How can you use factoring to find all the positive integers that could representthe values of the variables?List all factor pairs for 60. These are the possible values for the extremes.9. Find the solution to the problem.1 and 60; 2 and 30; 3 and 20; 4 and 15; 5 and 12; 6 and 10Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.2
NameClassDatePractice7-1Form GRatios and ProportionsWrite the ratio of the first measurement to the second measurement.1. diameter of a salad plate: 8 in.diameter of a dinner plate: 1 ft2. weight of a cupcake: 2 ozweight of a cake: 2 lb 2 oz3. garden container width: 2 ft 6 in.garden container length: 8 ft4. width of a canoe: 28 in.length of a canoe: 12 ft 6 in.5. height of a book: 11 in.height of a bookshelf: 3 ft 3 in.23117516147511396. The perimeter of a rectangle is 280 cm. The ratio of the width to the length is3 i 4. What is the length of the rectangle? 80 cm7. The ratio of country albums to jazz albums in a music collection is 2 i 3. If themusic collection has 45 albums, how many are country albums? 188. The lengths of the sides of a triangle are in the extended ratio 3 i 6 i 8. Thetriangle’s perimeter is 510 cm. What are the lengths of the sides? 90 cm, 180 cm, 240 cmAlgebra Solve each proportion.x139. 4 5 52 12b1112. 7 5 56 15xx1610. 2x 1 1 5 40 299x11. 10 5 70 791113. y 5 27 333m14. 34 5 51 4.56Use the proportion z 5 5 . Complete each statement. Justify your answer.uuuz17. x 5ux15. 6 5x1zz 5z5;Prop. of Proportions (2)16.56;Prop. of Proportions (1)18. 5x 5uu115;Prop. of Proportions (3)u 6z; Cross Products Property19. The measures of two consecutive angles in a parallelogram are in the ratio4 i 11. What are the measures of the four angles of the parallelogram?48, 48, 132, 132Prentice Hall Gold Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.3
Name7-1ClassDatePractice (continued)Form GRatios and ProportionsCoordinate Geometry Use the graph. Write each ratio in simplest form.AB 420. BD 7EC 322. BC 2AE 521. EC 323.yslope of BEslope of AEE621or 24224. A band director needs to purchase newA 4uniforms. The ratio of small to medium tolarge uniforms is 3 i 4 i 6.B 2a. If there are 260 total uniforms to purchase,how many will be small? 60OC246D x8 2b. How many of these uniforms will be medium? 80c. How many of these uniforms will be large? 12025. The measures of two complementary angles are in the ratio 2 i 3. What is themeasure of the smaller angle? 3626. The measures of two supplementary angles are in the ratio 4 i 11. What is themeasure of the larger angle? 13227. The means of a proportion are 4 and 17. List all possible pairs of positiveintegers that could be the extremes of the proportion. 1 and 68, 2 and 34, 4 and 1728. The extremes of a proportion are 5 and 14. List all possible pairs of positiveintegers that could be the means of the proportion. 1 and 70, 2 and 35, 5 and 14,7 and 10Algebra Solve each proportion.29.(x 2 1)105 14 6(x 1 1)7x30. 50 5 30 4.231. Writing Explain why solving proportions is an important skill for solvinggeometry problems. Answers may vary. Sample: Many geometric properties involveratios. You can use proportions to model them and solve problems.32. Draw a triangle that satisfies this condition: The ratio of the interior anglesis 7 i 11 i 12. Triangle should have angles that measure 42, 66, and 72.Prentice Hall Gold Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.4
NameClassDatePractice7-1Form KRatios and ProportionsWrite the ratio of the first measurement to the second measurement.1. length of car: 14 ft 10 in.2. weight of car: 2900 lblength of model car: 8 in.uweight of model car: 8 ozuu178 in.8914 ft 10 in.558 in.8 in.42900 lb2900 lb58 oz 5lb5800u3. diameter of car tire: 40 cm1uu124. height of car: 4 ft 8 in.height of toy car: 3 in. 56 i 3diameter of toy car tire: 18 mm 200 i 95. There are 238 juniors at a high school. The ratio of girls to boys in the juniorclass is 3 i 4. How many juniors are girls? How many are boys? 102; 1366. The sides of a rectangle are in the ratio 2 i 5. The perimeter of the rectangle is70 cm. What is the width of the rectangle? 10 cm7. The measures of the angles of a triangle are in the extended ratio 6 i 1 i 5.What is the measure of the largest angle? 90Algebra Solve each proportion. To start, use the Cross Products Property.x38. 5 5 25 1510.x99. 4 5 2 18x223 88 54yy163.611. 3 5 8aIn the diagram, b 5 23 . Complete each statement. Justify your answer.b12. a 53u2uau13.5 b32uProp. of Proportions (1)a1b14.5b5u3u2abProp. of Proportions (2)15.Prop. of Proportions (3)ba532u uProp. of Proportions (1)Prentice Hall Foundations Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.53
NameClass7-1DatePractice (continued)Form KRatios and ProportionsCoordinate Geometry Use the graph. Write each ratio insimplest form.uuyuu36AC16. AD 5; simplified to.84AB 117. EC 2E64218. slope of ED 23AOB2D xC46 219. You are helping to hang balloons in the gym for a school dance. There are atotal of 175 balloons. Some of the balloons are gold and the rest are silver. Ifthe ratio of gold to silver is 3 i 2, how many gold balloons are there? 10520. The ratio of the width to the height of a window is 2 i 7. The width of thewindow is 3 ft. Write and solve a proportion to find the height.275 x3 ; 10.5 ft21. The sides of a triangle are in the extended ratio of 3 i 4 i 10. If the length of theshortest side is 9 in., what is the perimeter of the triangle? 51 in.22. Write a proportion that has means 4 and 15 and extremes 6 and 10.Answers may vary. Sample: 64 5 1510Algebra Solve each proportion.x7723. 4 5 28 1125.3924. 4y 5 138 11.5635d11 3d158626. 2y 2 3 5 y 1 4 12.527. Writing Explain how the Cross Products Property can be used to show24that x 23 5 2x 1 1 is not a true proportion.Answers may vary. Sample: When you multiply the means and the extremesand simplify, you get 2 5 212, which is not true.Prentice Hall Foundations Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.68
NameClassDateStandardized Test Prep7-1Ratios and ProportionsGridded ResponseSolve each exercise and enter your answer on the grid provided.Use the graph at the right for Exercises 1 and 2.yAD1. What is AB in simplest form?6E422. What isslope of BEslope of AEAOin simplest form?B2D xC468 23. What is the value of x in the proportion(x 2 1)(4x 1 2)5535 ?x11154. What is the value of x in the proportion x 1 3 5 21 ?5. The lengths of the sides of a triangle are in the extended ratio 3 i 10 i 12. Theperimeter is 400 cm. What is the length of the longest side in centimeters?Answers1. 2.a01234567890123456789012345678901234567890 01 12 23 34 45 56 67 78 89 9 3.a01234567890123456789012345678901234567890 01 12 23 34 45 56 67 78 89 9 4.a01234567890123456789012345678901234567890 01 12 23 34 45 56 67 78 89 9 5.a01234567890123456789012345678901234567890 01 12 23 34 45 56 67 78 89 9Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.7 a01234567890123456789012345678901234567890 01 12 23 34 45 56 67 78 89 9
Name7-1ClassDateEnrichmentRatios and ProportionsRatios and proportions occur frequently in everyday situations. Some involvelinear equations, such as those concerning menu planning and recipes, whereasothers, often involving geometry, require quadratic equations.Use ratios and proportions to solve each problem.1. A meatloaf recipe uses 4 lb of hamburger to feed 6 people. How many poundsof hamburger will be used to feed 15 people? 10 lb2. The tenth grade at Milford High School has a dance every year. Last year therewere 80 students in the tenth grade, and the party cost 200. This year thereare 100 students in the tenth grade. How much should they plan to spend? 2503. If it costs 200,000 to build a sidewalk around a rectangular field whosedimensions are 200 yd by 800 yd, how much will it cost to build a sidewalkaround a rectangular field whose dimensions are 300 yd by 900 yd? 240,0004. The cost of buying a plot of land in Happy Valley depends on the area of theplot. If a rectangular plot of land whose dimensions are 200 yd by 800 yd costs 100,000, what is the cost of a rectangular plot of land whose dimensions are300 yd by 900 yd? 168,7505. If it costs 5980 to have a picket fence installed around a rectangular lot that is110 ft by 150 ft, how much will it cost to have a picket fence installed around arectangular lot that is 125 ft by 170 ft? 67856. At Pools-a-Plenty it costs 165 for a swimming pool cover for a round,aboveground pool that is 30 ft in diameter. How much will a cover for a poolthat is 24 ft in diameter cost at Pools-a-Plenty? Use 3.14 for p. 105.607. Fencing was purchased for two rectangular plots of land. The first plotmeasured 80 yd by 100 yd, and the cost of the fencing was 900. The cost ofthe fencing for the second plot was 2400, and one of the dimensions of theplot was 120 yd. What was the other dimension? 360 yd8. If 3 hens lay 10 eggs in 5 days, how many eggs will 3 hens lay in 20 days? 40 eggs9. If 8 hens lay 14 eggs in 6 days, how many eggs will 24 hens lay in 6 days? 42 eggs10. If 4 hens lay 7 eggs in 3 days, how many eggs will 12 hens lay in 9 days? 63 eggs11. If Jenna can walk 6 mi in 2 h, how many miles could she walk in 2.5 h,assuming she keeps the same pace? 7.5 mi12. Suppose 2.5 lb of grass seed can cover a plot of land that is 30 ft by 30 ft. Howmuch grass seed is needed to cover a plot of land 45 ft by 60 ft? 7.5 lbPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.8
NameClass7-1DateReteachingRatios and ProportionsProblemAbout 15 of every 1000 light bulbs assembled at the Brite Lite Company aredefective. If the Brite Lite Company assembles approximately 13,000 light bulbseach day, about how many are defective?Set up a proportion to solve the problem. Let x represent the number of defectivelight bulbs per day.15x1000 5 13,00015(13,000) 5 1000xCross Products Property195,000 5 1000xSimplify.195,0001000 5 xDivide each side by 1000.195 5 xSolve for the variable.About 195 of the 13,000 light bulbs assembled each day are defective.ExercisesUse a proportion to solve each problem.1. About 45 of every 300 apples picked at the Newbury Apple Orchard are rotten.If 3560 apples were picked one week, about how many apples were rotten? 5342. A grocer orders 800 gal of milk each week. He throws out about 64 gal ofspoiled milk each week. Of the 9600 gal of milk he ordered over three months,about how many gallons of spoiled milk were thrown out? 7683. Seven of every 20 employees at V & B Bank Company are between the ages of20 and 30. If there are 13,220 employees at V & B Bank Company, how manyare between the ages of 20 and 30? 46274. About 56 of every 700 picture frames put together on an assembly line havebroken pieces of glass. If 60,000 picture frames are assembled each month,about how many will have broken pieces of glass? 4800Algebra Solve each proportion.x3005. 1600 5 4800 900407006. 140 5 x 2450351508. x 5 2400 560x2909. 1040 5 5200 58x18011. 380 5 5700 12120027012. 90,000 5 x 20,250x177. 2000 5 400 85x8710. 42,000 5 500 7308325730613. x 5 56,200 2500Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.9
NameClassDateReteaching (continued)7-1Ratios and ProportionsIn a proportion, the products of terms that are diagonally across the equal signfrom each other are the same. This is called the Cross Products Property becausethe products cross at the equal sign.acb cda db c a d bProportions have other properties:acdacaSwitch b and c in the proportion.aca1bc1d5 d .bAdd the denominator to the numerator.Property (1) b 5 d is equivalent to ab 5 c .Use reciprocals of the ratios.bProperty (2) b 5 d is equivalent to c 5 d .Property (3) b 5 d is equivalent toProblemHow can you use the Cross Products Property to verify Property (3)?ac5 d is equivalent to ad 5 bc.ba1bc1d5 d is equivalent to (a 1 b)d 5 b(c 1 d) .bad 1 bd 5 bc 1 bdad 5 bcSo,Cross Products PropertyDistributive PropertySubtraction Property of Equalityaca1bc1d5 d is equivalent to b 5 d .bExercisesxUse the proportion 10 5 2z . Complete each statement. Justify your answer.x14. 2 510z ,uu1015. x 5Prop. of Proportions (2)z2,uuProp. of Proportions (1)16.x 1 1010 52 1 zz ,uuProp. of Proportions (3)17. The ratio of width to length of a rectangle is 7 i 10. The width of the rectangle is791 cm. Write and solve a proportion to find the length. 105 91x ; 130 cm18. The ratio of the two acute angles in a right triangle is 5 i 13. What is themeasure of each angle in the right triangle? 25, 65, 90Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.10
Name7-2ClassDateELL SupportSimilar PolygonsThere are two sets of note cards below that show how to solve for x,given LMNO M WXYZ, in the diagram at the right. The set on theleft explains the thinking and the set on the right shows the steps.Write the thinking and the steps in the correct order.WLXxM5O 3 N ZThink CardsWrite Cards15 5 xUse the Cross Products Property.45 5 3xSubstitute the values in theproportion.Divide each side by 3.MNON5XYZYSet up a proportion.535x9ThinkWriteONStep 1 MNXY 5 ZYFirst, you shouldset up a proportion.Step 2 x5 5 39Second, you shouldsubstitute the values in the proportion.Step 3 45 5 3xNext, you shoulduse the Cross Products Property.Step 4 15 5 xFinally, you shoulddivide each side by 3.Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.119Y
Name7-2ClassDateThink About a PlanSimilar PolygonsSports Choose a scale and make a scale drawing of a rectangular soccer field thatis 110 yd by 60 yd.1. What is a scale drawing? How does a figure in a scale drawing relate toan actual figure?Answers may vary. Sample: A scale drawing is enlarged or reduced proportionally tothe actual figure. A figure in a scale drawing and the actual figure are similar figures.2. What is a scale? What will the scale of your drawing compare? Write a ratio torepresent this.Answers may vary. Sample: a ratio of the actual size to the size in the drawing; the soccerfield’s actual length to the length in the drawing; actual length i length of drawing3. To select a scale you need to choose a unit for the drawing. Assuming you aregoing to make your drawing on a typical sheet of paper, which customary unitinchesof length should you use?4. You have to choose how many yards each unit you chose in Step 3 willrepresent. The soccer field is 110 yd long. What is the least number of yardseach unit can represent and still fit on an 8.5 in.-by-11 in. sheet of paper?Explain. Does this scale make sense for your scale drawing?The least number of yards each inch can represent is 10 yd. If the scale is 1 in. 5 10 yd,the scale drawing will be 11 in. long, which is the length of the paper. It might makesense to use a scale that makes the drawing smaller.5. Choose the scale of your drawing. Answers may vary. Sample: 1 in. 5 20 yd6. How can you use the scale to write a proportion to find the length of the fieldin the scale drawing? Write and solve a proportion to find the length of thesoccer field in the scale drawing.Answers may vary. Sample: Make a proportion using the actual length of the soccer110 yd20 ydfield, the length in the drawing, and the scale factor. in. 5 1 in. ; 5.5 in.7. Write and solve a proportion to find the width of the soccer field in the60 yd20 ydscale drawing. Answers may vary. Sample: w in. 5 1 in. ; 3 in.8. Use a ruler to create the scale drawing on a separate piece of paper.Check students’ work.Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.12
NameClassDatePractice7-2Form GSimilar PolygonsList the pairs of congruent angles and the extended proportion that relates thecorresponding sides for the similar polygons.1. ABCD , WXYZlA O lW , lB O lX ,lC O lY , lD O lZ ;ABWXBXACBCDA5 XY5 CDYZ 5 ZWZNOM5 NOST 5 TRTM3. NPOM , TQRSlN O lT , lP O lQ;lO O lR, lM O lS;ROMSQPNPOMN5 QR5 OMRS 5 STNPTQYD2. nMNO , nRSTlM O lR, lN O lS, lO O lT ;MNRSWRTOSDetermine whether the polygons are similar. If so, write a similarity statementand give the scale factor. If not, explain.M4.3333O6.K2.5NSU4.5ZY Hnot similar; corresponding ' not O4.5TMNOP M URST or MNOP M STUR; 2 i 3L6.49.6E32.56MEFW4.54.5NPX5.RHF3G9not similar; corresponding sides not proportionalDetermine whether the polygons are similar.7. an equilateral triangle with side8. a square with side length 4 andlength 6 and an equilateral trianglewith side length 15 yesa rectangle with width 8 andlength 8.5 no9. a triangle with side lengths 3 cm,10. a rhombus with side lengths 8 and4 cm, and 5 cm, and a triangle withside lengths 18 cm, 19 cm, and 20 cm noconsecutive angles 508 and 1308, anda rhombus with side lengths 13 andconsecutive angles 508 and 1308 yesPrentice Hall Gold Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.13G
Name7-2ClassDatePractice (continued)Form GSimilar Polygons11. An architect is making a scale drawing of a building. She uses the scale1 in. 5 15 ft.a. If the building is 48 ft tall, how tall should the scale drawing be? 3.2 in.b. If the building is 90 ft wide, how wide should the scale drawing be? 6 in.12. A scale drawing of a building was made using the scale 15 cm 5 120 ft. If thescale drawing is 45 cm tall, how tall is the actual building? 360 ftDetermine whether each statement is always, sometimes, or never true.13. Two squares are similar. always14. Two hexagons are similar. sometimes15. Two similar triangles are congruent. sometimes16. A rhombus and a pentagon are similar. neverAlgebra Find the value of y. Give the scale factor of the polygons.17. ABCD , TSVU7.5; 2 i 325.5S17AB3y 3.5D3y 3.517T3y 63y 6VC25.5U18. The scale factor of RSTU to VWXY is 14 i 3. What is the scale factor of VWXYto RSTU ? 3 i 14In the diagram below, kPRQ M kDEF . Find each of the following.19. the scale factor of nPRQ to nDEF 5 i 621. m/R 35204089 Q22. m/P 5623. DE 48DP20. m/D 5624F36R35 E24. FE 43.225. Writing Explain why all isosceles right triangles are similar, but not allscalene right triangles are similar. Answers may vary. Sample: All isosceles righttriangles have angle measures 45-45-90, the legs of the triangle will always becongruent, and the hypotenuses are always about 1.4 times the length of the leg.Scalene right triangles can have any pair of angle measures that adds up to 90 for thenon-right angles, so they are not all similar.Prentice Hall Gold Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.14
NameClassDatePractice7-2Form KSimilar PolygonsList the pairs of congruent angles and the extended proportion that relates thecorresponding sides for the similar polygons.1. ABCD , WXYZ2. nGHI , nKJLGWLAJZDXBYCulZ/D uu/C lYIulL/I u/B lX/A /WKHu/G lKu uu uDACDBCAB555WXXYYZZW/H lJIGHIuu5JLLKuuGHKJ 5Determine whether the polygons are similar. If so, write a similarity statementand give the scale factor. If not, explain.3.3C64QD86T3 EFCDEF M QRST; 3 i 44. QRSRS6.D84103UIB6MOVS12Rno; corresponding sides not proportional5.L4884T88 49 12N86 43 9HC49 4JkDBC M kJHI; 3 i 2U 3 Tno; corresponding sides not proportionalAlgebra The polygons are similar. Find the value of each variable.127.y128.615ab4x18997.2; 610126; 8Prentice Hall Foundations Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.15
Name7-2ClassDatePractice (continued)Form KSimilar Polygons9. You want to enlarge a 3 in-by-5 in. photo. The paper you will print on is8.5 in.-by-14 in. What is the largest size the photo can be? 8.4 in.-by-14 in.10. For art class, you need to make a scale drawing of the Parthenon using thescale 1 in. 5 ft. The Parthenon is 228 ft long. How long should you make thebuilding in your scale drawing? 45.6 in.11. Ella is reading a map with a scale of 1 in. 5 20 mi. On the map, the distanceElla must drive is 4.25 in. How many miles is this? 85 miAlgebra Find the value of z. Give the scale factor of the polygons.12. nJKL , nQRS 2; 1 i 39QK3Rz 4JzLS13. The scale factor of ABCD to EFGH is 7 i 20. What is the scale factor ofEFGH to ABCD? 20 i 7In the diagram below, kNOP M kWXY . Find each of the following.14. the scale factor of nNOP to nWXY 2 i 515. m/X 58WN16. m/Y 73NP 217. WY 518. WX 1549 12658 O4PYX1019. NP 4.820. A company makes rugs. Their smallest rug is a 2 ft-by-3 ft rectangle.Their largest rug is a similar rectangle. If one side of their largest rug is 18 ft,what are the possible dimensions of their largest rug? 18 ft-by-27 ft or 12 ft-by-18 ftPrentice Hall Foundations Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.16
NameClass7-2DateStandardized Test PrepSimilar PolygonsMultiple ChoiceFor Exercises 1–5, choose the correct letter.1. You make a scale drawing of a tree using the scale 5 in. 5 27 ft. If the tree is67.5 ft tall, how tall is the scale drawing? D10 in.11.5 in.12 in.12.5 in.2. You make a scale drawing of a garden plot using the scale 2 in. 5 17 ft. If thelength of a row of vegetables on the drawing is 3 in., how long is the actual row? G17 ft25.5 ft34 ft42.5 ft3. The scale factor of nRST to nDEC is 3 i 13. What is the scale factor of nDECto nRST ? D3 i 131 i 3939 i 113 i 34. nACB , nFED. What is the value of x? I22.5EDAx 4.4 23.5B9CF44.24.555. MNOP , QRST with a scale factor of 5 i 4. MP 5 85 mm. What is thevalue of QT? B60 mm68 mm84 mm106.25 mmShort Response6. Are the triangles at the right similar? Explain. A[2] Yes; corresponding angles arecongruent and lengths of correspondingsides are proportional. [1] recognition30that corresponding angles are congruentor corresponding side lengths areproportional. [0] No explanation given.CY33.51550.25B XPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.174522.5Z
NameClass7-2DateEnrichmentSimilar PolygonsFloor PlansArchitects, engineers, and other professionals make scale drawings to design orpresent building plans. A floor plan of the second floor of a house is shown below.Use the scale to find the actual dimensions of each room.1. playroom 18 ft by 10 ftBathroom2. library 18 ft by 14 ftClosetPlayroom3. master bedroom 18 ft by 16 ft4. bathroom 8 ft by 8 ftMasterBedroomLibrary5. closet 3 ft by 10 ftSomeone who wants to rearrange a room canmake use of a scale drawing of the room thatincludes furniture. Two-dimensional shapes canrepresent the objects that sit on the floor in the room.Scale: 1 in. 16 ftMake a scale drawing of a room in which you spend a lot of time, such as yourclassroom or bedroom, including any objects that take up floor space.6. Choose an appropriate scale so the drawing covers most of an 8.5 in.-by-11 in.piece of paper. What scale did you choose?Answers may vary. Sample: 1 in. 5 3 ft7. What shape is the room? Measure the dimensions of the room and draw theshape to represent the room’s outline.Answers may vary. Sample: rectangle; 15 ft by 24 ft8. List three objects that take up floor space. Measure the dimensions of eachobject, then determine their dimensions in the scale drawing. You can roundto the nearest millimeter or quarter of an inch.ObjectActual DimensionsScale FactorDimensions on DrawingSample: tableSample: 4 ft by 8 ft192 i 1Sample: 0.25 in. by 0.50 in.9. Complete the scale drawing. Remember to measure the distance betweenobjects so that this is accurately represented in the drawing. Check students’ work.Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.18
NameClassDateReteaching7-2Similar PolygonsSimilar polygons have corresponding angles that are congruent andcorresponding sides that are proportional. An extended proportion can bewritten for the ratios of corresponding sides of similar polygons.ProblemAre the quadrilaterals at the right similar? If so, write a similaritystatement and an extended proportion.B/A /X , /B /Y ./C /Z, /D /WCompare angles:6ABXY 5 3 5 2BC8YZ 5 4 5 2Compare ratios of sides:C896CD9ZW 5 4.5 5 2DA4WX 5 2 5 2Y34AX 2 WDBecause corresponding sides are proportional and corresponding angles arecongruent, ABCD , XYZW .The extended proportion for the ratios of corresponding sides is:BCCDABDAXY 5 YZ 5 ZW 5 WXExercisesIf the polygons are similar, write a similarity statement and the extendedproportion for the ratios of corresponding sides. If the polygons are not similar,write not CA M YZX, BCYZ 5 ZX 5 XYKML M QSR, QS 5 SR 5 RQ3. P1428302060KMZB4030Y2124187J7L R 77not similarPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.19P760 Mnot similarN7 77VK4QZ4.5
NameClassDateReteaching (continued)7-2Similar PolygonsProblemnRST , nUVW. What is the scale factor?TWhat is the value of x?74RW2S6xUVIdentify corresponding sides: RT corresponds to UW , TS corresponds to WV , andSR corresponds to VU .TSRTUW 5 WVCompare corresponding sides.7425xSubstitute.4x 5 14Cross Products Propertyx 5 3.5Divide each side by 4.7The scale factor is 42 5 3.5 5 2. The value of x is 3.5.ExercisesGive the scale factor of the polygons. Find the value of x. Round answers to thenearest tenth when necessary.5. ABCD , NMPO 5 i 3; 3.64A6. nXYZ , nEFD 3 i 2; 9.3B15XM 2.4 N56OMxL209.8NPR1411.5E8. OPQRST , GHIJKL 4 i 3; 12QO10FZ7. LMNO , RQTS 10 i 7; 8.1TxOxCLD143PDYQT20SSK9Jx RPrentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.20G15I15H
NameClassDateELL Support7-3Proving Triangles SimilarThe column on the left shows the steps used to solve a proportion. Use thecolumn on the left to answer each question in the column on the right.1. Look at the diagram. What measureSAS M TheoremProblemare you trying to find?Use a proportion to find x.B4AThe length of EF is unknown.E8x87C D16F2. What is the SAS , Theorem?Verify that the triangles are similar.848 5 16If an angle of one triangle is/A /Dcongruent to an angle of a secondnABC , nDEF by SAS , Theorem.triangle, and the sides that includethe two angles are proportional,then the triangles are similar.Write a proportion.3. What is a proportion?7485xA proportion is an equation thatstates that two ratios are equal.Write the cross products.4. What does writing the crossproducts mean?4?x58?7The cross products of a proportionSimplify.are equal. First multiply the extremes4x 5 56of the proportion to get theproduct for one side of the equation,and then multiply the means toget the product of the other side ofthe equation.Divide both sides by 4.5. Why do you divide both sides by 4?To isolate the variable x.x 5 14Prentice Hall Geometry Teaching ResourcesCopyright by Pearson Education, Inc., or its affiliates. All Rights Reserved.21
NameClassDateThink About a Plan7-3Proving Triangles SimilarIndirect Measurement A 2-ft vertical post casts a 16-in. shadow at the same timea nearby cell phone tower casts a 120-ft shadow. How tall is the cell phone tower?Answers may vary. Sa
You are helping to hang balloons in the gym for a school dance. Th ere are a total of 175 balloons. Some of the balloons are gold and the rest are silver. If the ratio of gold to silver is 3i2, how many gold balloons ar
