NAME DATE PERIOD. 10. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet.

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1 6-1 IO ractice roportions 1. IIO One ounce of cheddar cheese contains grams of fat. i of the grams of fat are saturated fats. ind the ratio of saturated fats to total fat in an ounce of cheese.. I he ratio of goats to sheep at a university research farm is :7. he number of sheep at the farm is 8. hat is the number of goats?. dward opper s oil on canvas painting ighthawks has a length of 60 inches and a width of 0 inches. print of the original has a length of.5 inches. hat is the width of the print? olve each proportion ind the measures of the sides of each triangle. 10. he ratio of the measures of the sides of a triangle is ::6, and its perimeter is 10 feet. 11. he ratio of the measures of the sides of a triangle is 7::, and its perimeter is 8 inches.. he ratio of the measures of the sides of a triangle is 6:7:, and its perimeter is 77 centimeters. ind the measures of the angles in each triangle. 1. he ratio of the measures of the angles is :5:6.. he ratio of the measures of the angles is 5:7: I he span of the enjamin ranklin suspension bridge in hiladelphia, ennsylvania, is 1750 feet. model of the bridge has a span of inches. hat is the ratio of the span of the model to the span of the actual enjamin ranklin ridge? lencoe/craw-ill 8 lencoe eometry

2 6- IO kills ractice imilar olygons etermine whether each pair of figures is similar. ustify your answer Z X ach pair of polygons is similar. rite a similarity statement, and find, the measure(s) of the indicated side(s), and the scale factor... and X 5 5 esson and V lencoe/craw-ill 0 lencoe eometry

3 6- IO ractice imilar riangles etermine whether each pair of triangles is similar. ustify your answer Identify the similar triangles, and find and the measures of the indicated sides.. and. and se the given information to find each measure. 5. If, 6, 7, 6. If I,, 1, 8, and 1, I, and, find and. find and. I II or ercises 7 and 8, use the following information. lighthouse casts a 8-foot shadow. nearby lamppost that measures 5 feet inches casts an 8-foot shadow. 7. rite a proportion that can be used to determine the height of the lighthouse. 8. hat is the height of the lighthouse? lencoe/craw-ill 10 lencoe eometry

4 IO 6- kills ractice arallel ines and roportional arts 1. If 7, 1, and 6,. ind and V if 8,, find I. V 1 and V 1. V I etermine whether.. 15,, 10, and 8., 7, and is one third of 5. 0, 5, and is twice OOI O or ercises 6 8, use the following information. riangle has vertices ( 5, ), (1, 8), and (, ). oint is the midpoint of and is the midpoint of. y 6. Identify the coordinates of and. O 7. how that is parallel to. 8. how that 1. esson 6-. ind and y. 10. ind and y. 1 y 8 7 y 5 y 1 y 5 lencoe/craw-ill 15 lencoe eometry

5 6-5 IO ractice arts of imilar riangles ind the perimeter of the given triangle. 1., if, 6,., if,, 0, 0, and 5 1,, and 8 se the given information to find each measure.. ind if, is an. ind Z if XZ, is an altitude of, is an altitude of altitude of, Z is an altitude of, 8,, and XZ, 8.5, 6, and Z 11.. Z X ind OO or ercises 7 and 8, use the following information. rancine has a camera in which the distance from the lens to the film is millimeters. 7. If rancine takes a full-length photograph of her friend from a distance of meters and the height of her friend is 0 centimeters, what will be the height of the image on the film? (int: onvert to the same unit of measure.) 8. uppose the height of the image on the film of her friend is 15 millimeters. If rancine took a full-length shot, what was the distance between the camera and her friend? lencoe/craw-ill lencoe eometry

6 6-6 IO kills ractice ractals and elf-imilarity tages 1 and of a fractal known as the antor set are shown. o get tage, the segment in tage 1 is trisected, and the interior of the middle segment is removed. (he interior of a segment is the segment with its endpoints removed.) he process is repeated for subsequent stages. tage 1 tage esson raw stages and of the antor set. tage tage. ow many segments are there in tage? tage?. hat happens to the length of the line segments in each stage?. he antor set is the set of points after infinitely many iterations. Is the antor set self-similar? ind the value of each epression. hen, use that value as the net in the epression. epeat the process three times, and describe your observations. 5., where initially equals 5 6., where initially equals 1 ind the first three iterates of each epression. 7. 1, where initially equals 8. 1, where initially equals 8 lencoe/craw-ill 7 lencoe eometry

7 nswers (esson 6-1) 6-1 IO kills ractice roportions lencoe/craw-ill 7 lencoe eometry nswers esson OO tight end scored 6 touchdowns in games. ind the ratio of touchdowns per game. 0.:1. IO In a schedule of 6 classes, arta has elective classes. hat is the ratio of elective to non-elective classes in arta s schedule? 1:. IOO Out of 7 listed species of birds in the nited tates, 78 species made the endangered list. ind the ratio of endangered species of birds to listed species in the nited tates n artist in ortland, Oregon, makes bronze sculptures of dogs. he ratio of the height of a sculpture to the actual height of the dog is :. If the height of the sculpture is inches, find the height of the dog. 1 in. 5. OO he ratio of male students to female students in the drama club at ampbell igh chool is :. If the number of male students in the club is, what is the number of female students? olve each proportion ind the measures of the sides of each triangle.. he ratio of the measures of the sides of a triangle is :5:7, and its perimeter is 50 centimeters. 0 cm, 150 cm, 10 cm 1. he ratio of the measures of the sides of a triangle is 5:6:, and its perimeter is 0 meters. 55 m, 66 m, m. he ratio of the measures of the sides of a triangle is :6:8, and its perimeter is 6 feet. 8 ft, ft, 56 ft 15. he ratio of the measures of the sides of a triangle is 5:7:8, and its perimeter is 0 inches. 10 in., in., 16 in. IO 6-1 ractice (verage) roportions 1. IIO One ounce of cheddar cheese contains grams of fat. i of the grams of fat are saturated fats. ind the ratio of saturated fats to total fat in an ounce of cheese. :. I he ratio of goats to sheep at a university research farm is :7. he number of sheep at the farm is 8. hat is the number of goats? 16. dward opper s oil on canvas painting ighthawks has a length of 60 inches and a width of 0 inches. print of the original has a length of.5 inches. hat is the width of the print? 1.5 in. olve each proportion ind the measures of the sides of each triangle. 10. he ratio of the measures of the sides of a triangle is ::6, and its perimeter is 10 feet. ft, ft, 8 ft 11. he ratio of the measures of the sides of a triangle is 7::, and its perimeter is 8 inches. 1 in., 7 in., 6 in.. he ratio of the measures of the sides of a triangle is 6:7:, and its perimeter is 77 centimeters. 1 cm,.5 cm, 1.5 cm ind the measures of the angles in each triangle. 1. he ratio of the measures of the angles is :5:6. 8, 60, 7. he ratio of the measures of the angles is 5:7:8. 5, 6, I he span of the enjamin ranklin suspension bridge in hiladelphia, ennsylvania, is 1750 feet. model of the bridge has a span of inches. hat is the ratio of the span of the model to the span of the actual enjamin ranklin ridge? lencoe/craw-ill 8 lencoe eometry lencoe/craw-ill lencoe eometry

8 esson 6-6- IO kills ractice imilar olygons etermine whether each pair of figures is similar. ustify your answer Z X ;, rhombus rhombus XZ;, and, X,, because if two angles of one Z; triangle are congruent to two angles of a second triangle, then the third angles are congruent;. X X Z Z ach pair of polygons is similar. rite a similarity statement, and find, the measure(s) of indicated side(s), and the scale factor... and X 5 5 ; X (or ) 6 1 ;6 1 ; 7;; ; and V 10 1 V; ; 5; 6; 1; ; 15; lencoe/craw-ill 0 lencoe eometry etermine whether each pair of figures is similar. ustify your answer V ; V;,,, V, and by the,, and hird ngle heorem and 5 or 1.67 V V. ach pair of polygons is similar. rite a similarity statement, and find, the measure(s) of indicated side(s), and the scale factor.. and. and ; ; ;10 1 ;7 1 ; 7; ; 8; 5. OOI O riangle has vertices (0, 0), (, 0), and (, ). he coordinates of each verte are multiplied by to create. how that is similar to., 5 and, ; and since, and. ince the corresponding angles are congruent and the corresponding sides are proportional,. 6. IIO I raham used the scale drawing of his living room to decide where to place furniture. ind the dimensions of the living room if the scale in the drawing is 1 inch.5 feet. ft by 11 ft in. in. 1 in. lencoe/craw-ill 0 lencoe eometry nswers (esson 6-) IO 6- ractice (verage) imilar olygons lencoe/craw-ill 6 lencoe eometry

9 nswers (esson 6-) 6- IO kills ractice imilar riangles lencoe/craw-ill 0 lencoe eometry nswers esson 6- etermine whether each pair of triangles is similar. ustify your answer X o; the sides are not proportional. yes; (or ); imilarity yes; ; yes; ; imilarity imilarity Identify the similar triangles, and find and the measures of the indicated sides. 5. and 6. and ; 15; 16; 0 ; 10; 8; 7 7. and 8. and 6 5 V 6 6 ; ;; V; ; 6; IO 6- ractice (verage) imilar riangles etermine whether each pair of triangles is similar. ustify your answer yes; ; o; the sides are not proportional. imilarity Identify the similar triangles, and find and the measures of the indicated sides.. and. and ; ;; 8 ; ;1; se the given information to find each measure. 5. If, 6, 7, 6. If I,, 1, 8, and 1, I, and, find and. find and. I ; 16 6; 8 II or ercises 7 and 8, use the following information. lighthouse casts a 8-foot shadow. nearby lamppost that measures 5 feet inches casts an 8-foot shadow. 7. rite a proportion that can be used to determine the height of the lighthouse. ample answer: If height of lighthouse, hat is the height of the lighthouse? 8 ft lencoe/craw-ill 10 lencoe eometry lencoe/craw-ill lencoe eometry

10 nswers (esson 6-) esson 6-6- IO kills ractice arallel ines and roportional arts 1. If 7, 1, and 6,. ind and V if 8,, find I. V 1 and V 1. V I 11; 10 etermine whether.. 15,, 10, and 8 yes., 7, and is one third of no 5. 0, 5, and is twice yes OOI O or ercises 6 8, use the following information. riangle has vertices ( 5, ), (1, 8), and (, ). oint is the midpoint of and is the midpoint of. y 6. Identify the coordinates of and. (, 5); ( 0.5, ) O 7. how that is parallel to. ince the slope of is and the slope of is, is parallel to. 8. how that 1. 5 he length of is 11.5 or and the length of is 5.. ind and y. 10. ind and y. 1 y 8 7 y 5 y 1 y 5 6, y 6.5, y lencoe/craw-ill 15 lencoe eometry IO 6- ractice (verage) arallel ines and roportional arts 1. If, 7, and,. ind,, and if 6, find., 7, and. 16 ; ; 8 etermine whether.., 0, 1, and 5 no.,, and 5 6 yes OOI O or ercises 5 and 6, use the following information. riangle has vertices (, 1), (, 5), and (, 1). oint is the midpoint of and is the midpoint of. 5. how that is parallel to. he slope of is 1 and the slope of is 1, so is parallel to. O y 6. how that 1. he length of is, and the length of is ind and y. 8. ind and y. y 5 1 y 6 y y 1, y 5, y. he distance from ilmington to sh rove along endall is 80 feet and along agnolia, 660 feet. If the distance between eech and sh rove along agnolia is 80 feet, what is the distance between the two streets along endall? about 8 ft ilmington agnolia endall eech sh rove lencoe/craw-ill 16 lencoe eometry lencoe/craw-ill lencoe eometry

11 nswers (esson 6-5) 6-5 IO kills ractice arts of imilar riangles lencoe/craw-ill 1 lencoe eometry nswers esson 6-5 ind the perimeter of the given triangle. 1., if,,., if, 7,, 10, and 16, 5, and , if, 16,., if, 0,, 7, and 8, 8, and se the given information to find each measure. 5. ind if, is an 6. ind if, is an altitude of, is an altitude of altitude of, is an altitude of, 6, 5, and 7.,,, and ind. 7. XZ X Z IO 6-5 ractice (verage) arts of imilar riangles ind the perimeter of the given triangle. 1., if, 6,., if,, 0, 0, and 5 1,, and se the given information to find each measure.. ind if, is an. ind Z if XZ, is an altitude of, is an altitude of altitude of, Z is an altitude of, 8,, and XZ, 8.5, 6, and Z 11.. Z X ind OO or ercises 7 and 8, use the following information. rancine has a camera in which the distance from the lens to the film is millimeters. 7. If rancine takes a full-length photograph of her friend from a distance of meters and the height of her friend is 0 centimeters, what will be the height of the image on the film? (int: onvert to the same unit of measure.) 11. mm 8. uppose the height of the image on the film of her friend is 15 millimeters. If rancine took a full-length shot, what was the distance between the camera and her friend?. m lencoe/craw-ill lencoe eometry lencoe/craw-ill 15 lencoe eometry

12 nswers (esson 6-6) esson IO kills ractice ractals and elf-imilarity tages 1 and of a fractal known as the antor set are shown. o get tage, the segment in tage 1 is trisected, and the interior of the middle segment is removed. (he interior of a segment is the segment with its endpoints removed.) he process is repeated for subsequent stages. tage 1 tage 1. raw stages and of the antor set. tage tage. ow many segments are there in tage? tage? segments; 8 segments. hat happens to the length of the line segments in each stage? he line segments decrease in length by two-thirds at each stage.. he antor set is the set of points after infinitely many iterations. Is the antor set self-similar? yes ind the value of each epression. hen, use that value as the net in the epression. epeat the process three times, and describe your observations. 5., where initially equals 5 (5) 7; (7) 11; (11) 1; (1) 5 he iterates increase by consecutive powers of. 6., where initially equals ; ; ; he iterates are halved with each iteration, approaching zero. ind the first three iterates of each epression. 7. 1, where initially equals 8. 1, where initially equals 8, 8, 6 0.5, 8, 0.5 lencoe/craw-ill 7 lencoe eometry IO 6-6 n artist is designing a book cover and wants to show a copy of the book cover in the lower left corner of the cover. fter tages 1 and of the design, he realizes that the design is developing into a fractal! tage 1 ractice (verage) ractals and elf-imilarity tage 1. raw tages and of the book cover fractal. tage tage. fter infinitely many iterations, will the result be a self similar fractal? yes. On what part of the book cover should you focus your attention to be sure you can find a copy of the entire figure? the lower left corner ind the value of each epression. hen, use that value as the net in the epression. epeat the process three times and describe your observations.. ( ), where initially equals 0 5., where initially equals 10 6,,, 0,,, 5 he difference between values he difference between values is doubles with each term. multiplied by 1 with each term. ind the first three iterates of each epression. 6. 1, where initially equals 1 7., where initially equals 1.5; 1.75; ; 8;, OI he ndrews purchased a house for $6,000. he real estate agent who sold the house said that comparable houses in the area appreciate at a rate of.5% per year. If this pattern continues, what will be the value of the house in three years? ound to the nearest whole number. $10,55 lencoe/craw-ill 8 lencoe eometry lencoe/craw-ill lencoe eometry