Geometry LM 12-4 through 12-6B
Geometry LM 12-4 through 12-6B
Geometry LM 12-4 through 12-6B
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NameL E S S O NM A S T E RVocabulary<strong>12</strong>-4BQuestions on SPUR Objectives1. a. What is a ratio?b. Give three examples of ratios.2. a. What is a proportion?b. Give three examples of proportions.c. Write a proportion and labelits means and its extremes.Skills Objective B: Use proportions to find missing parts in similar figures.UCSMP <strong>Geometry</strong> © Scott, Foresman and Company3. AWD is the image of UPO under asize change. Write three equal ratiosinvolving the sides of these triangles.In 4 and 5, MGT is the image of VRSunder a size change.4. If MG 14, VR 10,and MT 21, find VS.5. Multiple choice. Whichequation is a proportion?ADMWUORVPGT VSMT VS(a)RSMT(b)GTVRGSGT MTMT(c)RSVS(d)GTVRRST189
Name LESSON MASTER <strong>12</strong>-4B page 2In 6 and 7, UVWXYZ is the image ofABCDEF under a size change.6. If XY 20.4, FA 42, andDE 30.6, find ZU.7. If WX 30, VU 44, and BA 67.5,what other segment length can youdetermine? Find that length.CFDWZEA VXYUBUses Objective E: Identify and determine proportional lengths and distances inreal situations.8. If 2.5 pounds of roast beef cost $9.98, whatshould 6 pounds of roast beef cost?9. A computer printer prints 100 pages in<strong>12</strong> minutes. At that rate, how long would ittake to print 750 pages?10. If you read p pages in 10 hours, at that rate,how many pages can you read in s hours?11. A souvenir model of the Eiffel Tower in Paris is1the actual size. If the model is 15 cm tall,2000how many meters high is the Eiffel Tower?<strong>12</strong>. The dilution rate for plant fertilizer is 1.5 oz offertilizer to each 32 oz of water. How much watershould be used for the full 24-oz bottle of fertilizer?Review Objective D, Lesson 4-5, and Objective A, Lesson <strong>12</strong>-213. At the right draw r k ° r ( ABC ).uLabel the image DEF. Thendraw S 2(DEF) with center O.Label the image GHI. Howdo the lengths of the sides ofGHI compare to the lengthsof the sides of ABC?ACBOEHFDIGUCSMP <strong>Geometry</strong> © Scott, Foresman and Companyuk190
NameL E S S O NM A S T E RVocabulary<strong>12</strong>-5BQuestions on SPUR Objectives1. Define similar figures.2. What is a similarity transformation?3. What is a ratio of similitude?Skills Objective B: Use proportions to find missing parts in similar figures.UCSMP <strong>Geometry</strong> © Scott, Foresman and Company4. XYZ is the image of DEFunder a similarity transformation.Find each of the following.a. YZb. DFc. anotherangle measured. a ratio ofsimilitude5. QTSR POMN. Find as manymissing lengths as possible.X40°2016QDY<strong>12</strong>8ZF24T916SP 810ENMOR191
Name LESSON MASTER <strong>12</strong>-5B page 26. GYT UFZ, with the ratio of similitude 4.5,FZ 31.5, and GT 5.a. Find as many other segment lengthsas possible.b. If m∠Y 62 and m∠Z 40, find as manyother angle measures as possible.7. Parallelograms ABCD and DEFG are similar.a. Complete the following. The ratio ofsimilitude is ? or ? .b. Find BC.c. Find m∠A.28AD30GBCE75°F40Uses Objective E: Identify and determine proportional lengths and distances inreal situations.8. A slide measures 35 mm by 23 mm. The full pictureis projected on a screen and measures <strong>12</strong>0 cm long.What is the width of the picture on the screen?9. Lucy is 5 ft 5 in. tall and her little sister Gwen is4 ft 2 in. tall. In a photograph of the two sisters, Lucyis 6.25 in. tall. How tall is Gwen in the photograph?10. A scale model of the solar system shows Mercury24 inches from the sun. The actual distance isabout 36 million miles. Earth is about 93 millionmiles from the sun. In the model, how far shouldEarth be from the sun?11. On the 2-in.-by-2-in. photograph of a United Statespassport, the size of a person’s face from the chin tothe top of the head must not be less than 1 in. nor3greater than 18in. If a person’s face measures 3.5 in.in a photograph, by what range of scale factors mustthe photograph be reduced for use on a passport?UCSMP <strong>Geometry</strong> © Scott, Foresman and Company192
NameL E S S O NM A S T E R<strong>12</strong>-<strong>6B</strong>Questions on SPUR ObjectivesProperties Objective D: Use the Fundamental Theorem of Similarity to findlengths, perimeters, areas, and volumes in similarfigures.1. At the right, ABCD UVWX.a. What is the ratioof similitude?b. What is the ratioof their perimeters?c. What is the ratioof their areas?XU18WVAD<strong>12</strong>CB2. EFGHIJ ONMLKJ with a3ratio of similitude of5. Thearea of EFGHIJ is 32 squareunits and the perimeter ofOMNLKJ is 14 units.a. What is the areaof OMNLKJ?GHFIEJOKN<strong>LM</strong>b. What is the perimeterof EFGHIJ?3. Two figures are similar with a ratio of similitude of 4.2.UCSMP <strong>Geometry</strong> © Scott, Foresman and Companya. What is the ratio of corresponding lengths?b. What is the ratio of their perimeters?c. What is the ratio of their areas?d. What is the ratio of their volumes?e. What is the ratio of correspondingangle measures?193
Name LESSON MASTER <strong>12</strong>-<strong>6B</strong> page 24. Two quadrilaterals are similar and have perimetersof 33 cm and 13.2 cm. If the area of the largerquadrilateral is 61.5 cm 2 , find the area of the smaller.5. Two rectangles are similar. The width of the smallerone is 8 ft and the width of the larger is 10 ft. If thearea of the larger rectangle is 660 ft 2 , what is thelength of the smaller rectangle?6. Two right triangles are similar and have areas of36 m 2 and 144 m 2 . If the hypotenuse of the largertriangle is 30 m long, what is the length of thehypotenuse of the smaller triangle?Uses Objective F: Apply the Fundamental Theorem of Similarity in real situations.7. A drawing was enlarged 250% on a copy machine.What is the ratio of the areas of the two drawings?8. A toy train set is 1.5% the size of the actual train.If the volume of the toy boxcar is about <strong>12</strong>.3 in 3 ,what is the volume of the actual boxcar?9. Two solid busts of Beethoven are similar and madeout of the same material. Their heights are 22 cmand 38 cm. If the smaller bust weighs 14 kg,what is the weight of the larger?10. A parade featured a 7-meter-tall balloon of PerkyPenguin. Plastic souvenirs, similar to the balloon,were <strong>12</strong> cm tall. If the surface area of the souvenir is600 cm 2 , what is the surface area of the large balloon?11. The kites at the right are similar. Theirareas are 1900 in 2 and 1372.75 in 2 . If thelonger brace of the larger kite is 4 ft 2 in.long, what is the length of the longer braceof the smaller kite?UCSMP <strong>Geometry</strong> © Scott, Foresman and Company194
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