Geometry Chapter 13 Lesson Master Bs

NameL E S S O NM A S T E RVocabulary13-1BQuestions on SPUR Objectives1. State the SSS Similarity Theorem.Properties Objective F: Determine whether or not triangles are similar usingthe SSS Similarity Theorem.In 2–5, true or false.2. Triangles with sides measuring 3, 5, and 7 and6, 10, and 14 are similar.3. Triangles with sides measuring 1.5, 1.5, and3.5 and 6, 10, and 12 are similar.4. Triangles with sides measuring 5 ft, 6 ft, and 7 ftand 6 ft, 5 ft, and 7 ft are similar.5. Triangles with sides measuring 3 cm, 4 cm, and 5 cmand 6 m, 8 m, and 10 m are similar.UCSMP Geometry © Scott, Foresman and CompanyIn 6–13, determine whether or not the triangles in eachpair are similar. If so, write a similarity statement usingthe correct order of vertices. Justify your answer.6. C D 3.6 F 7.A1.8 22.43 2.7BEX4Y46Z1212U8V197

Name LESSON MASTER 13-1B page 28. J9.4G23K1.52.1 1.5LHT4848P 27 A36 36R10. M11.64QP6.54 6NO13O21PR35262519QTS1512. A13.12D1824E 206B 40 CEReview Previous Course and Objective B, Lesson 12-414. Consider the a. Name the means. b. Name the extremes.proportion1272.18 108c. Write three other proportionsusing these numbers.24D3x12F8G2x16HUCSMP Geometry © Scott, Foresman and Company15. Ifac, give a.a bc db.a bb db dban instance ofeach case.c dd198

NameL E S S O NM A S T E RVocabulary13-2BQuestions on SPUR Objectives1. State the AA Similarity Theorem.2. State the SAS Similarity Theorem.3. Explain why there is no ASA Similarity Theorem.Properties Objective F: Determine whether or not triangles are similar usingthe AA and SAS Similarity Theorems.In 4–9, determine whether or not the triangles in eachpair are similar. If so, write a similarity statementusing the correct order of vertices. Justify your answer.UCSMP Geometry © Scott, Foresman and Company4. CF5.50°65° EABD6. R 8P7.20 20S50QX15YL24O2030ZVM64U22.5N199

Name LESSON MASTER 13-2B page 28. P9.30Q3015R15ISA4B8C16D10. At a ground distance of 1.5 miles from takeoff, a plane’saltitude is 1000 yards. Assuming a constant angle ofascent, find the plane’s altitude 5 miles from takeoff.11. Use the information in the diagramto find the width of the river.12. A man standing 5 meters from a 6-meter pole casts a2.5-meter shadow, the tip of which aligns with the tipof the pole’s shadow. How tall is the man?160 mCrystal River80 m40 m13. The diagram shows how an archaeologistcan find the original height of a pyramid,even though its top has worn away. Findthe original height of the pyramid.14. A tourist on the observation deck of an 800-footbuilding looks toward a 600-foot building whichis one block away. Her car is parked two blocksbeyond the shorter building. If no other buildingintervenes, can she see her car?15. The foot of a ladder is 1.2 m from a 1.8-m-highfence. The ladder touches the fence and restsagainst a building 1.8 m behind the fence.a. Draw a diagram of the situation.40 m45 m60 mUCSMP Geometry © Scott, Foresman and Companyb. Determine how far up thebuilding the top of theladder can reach.c. How long is the ladder?1.8 m1.2 m 1.8 m200

NameL E S S O NM A S T E R13-3BQuestions on SPUR ObjectivesVocabularyIn 1 and 2, complete the Side-Splitting Theorem andits converse.1. If a line is ? to a side of a triangle andintersects the other two sides in distinct points,it splits these sides into ? segments.2. If a line intersects OP and OQ inOX OYdistinct points X and Y so thatXPYQ,then XY is to PQ.3. At the right, draw a picture of thesituation in Question 2.Skills Objective A: Find lengths in figures by applying the Side-Splitting Theoremand the Side-Splitting Converse Theorem.P84XO5Y10Q4. Given XYZ at the right, in which RS // YZ,find each missing length.Xa. XR 8; XS 6; XZ 15; XY SRUCSMP Geometry © Scott, Foresman and Companyb. XS 6; XR 9; XY 15; XZ c. XS 6; SZ 4; XR 8; RY d. XR 6n; RY 2n; XS 9; SZ 5. In the diagram at the right, h // j // k. Find eachmissing length.a. AC 9; BC 6; DF 15; EF b. AB 4; BC 13; EF 39; DE c. AB 5y; DE 2y; EF 12; BC 6. Given ADM at the right, in which OP // AD,tell whether each statement is true.ZDEFMxABCzYhjkx za. ywx yb. z wy zOyAPwD201

Name LESSON MASTER 13-3B page 27. Name all pairs of parallel lines in thefigure at the right.L 24 M 16 N 20 O30S18R24QP2030Uses Objective H: Use the Side-Splitting Theorem to find lengths and distances inreal situations.8. A half-mile ramp begins 2596 ftfrom a bridge. There is a supportunder a toll plaza which is located1500 ft up the ramp.1500'a. How far is the base of the supportfrom the lower end of the ramp?2596'b. How high is the support?9. Residents are to pay for newcurbs in proportion to thefootage their lots have onLatrobe. What part of thetotal cost must be paid byeach resident?Jones Kyoto Garcia Wills10. In the street map at the right,River Street is parallel to LakeStreet and Pond Street. Theintersection of River and Stateis 1200 ft from the intersectionof Lake and State, and theintersection of Pond and Stateis another 800 ft. Theintersection of Foster and Pondis 1000 ft from Foster andLake. How far is it from Fosterand Lake to the intersection ofFoster and River?196'Jones192'FosterLATROBE147'Kyoto Garcia Wills96'WILLOW ROADState49'RiverLakePondUCSMP Geometry © Scott, Foresman and Company202

NameL E S S O NM A S T E R13-4BQuestions on SPUR ObjectivesVocabularyIn 1 and 2, given the positive numbers a and b,1. define the geometric mean.2. define the arithmetic mean.3. For the set {4, 9}, find thea. arithmetic mean. b. the geometric mean.4. State the Right-Triangle Altitude Theorem.Skills Objective B: Calculate lengths using the Right-Triangle Altitude Theorem.5. Given MOP at the right, find each length.a. MP 3; MN 12; MO OUCSMP Geometry © Scott, Foresman and Companyb. PN 4; MN 9; ON c. PN 28; PM 7; OP d. OP 8; MP NP; MN 6. Given the diagram at the right, find each length.a. a 30; c 50; h b. h 12; m 9; b c. a 24; m 4; b MPamchnbNd. b 8; m 12; c 7. Find d in the diagram at the right.1516d5203

Name LESSON MASTER 13-4B page 28. Use the diagram at the right to find each length.a. a 7 5; h 14; c ; n b. a 6 5; b 3 5; m ; n am chnbReview Objective D, Lesson 5-7, and Objective D, Lesson 8-69. Find the sum of the measures of the anglesin a 15-sided polygon.10. Polygon PQRSTU at the right is a regularhexagon. Give the measure of each angle.a. m∠OPQUPOQRb. m∠ROTTS11. Polygon ABCDEFGH at the right is a regularoctagon. Give the measure of each angle.a. m∠ODEGHAOBb. m∠DOCFCEDIn 12–15, find the missing length.12. 13.8814. 15.5 3 512 2812UCSMP Geometry © Scott, Foresman and Company4 3204

NameL E S S O NM A S T E RVocabulary13-5BQuestions on SPUR Objectives1. In the diagram at the right,Eis inscribed in .DAIn 2 and 3, complete the theorems.2. According to the Isosceles Right Triangle Theorem,in an isosceles right triangle,COB3. The 30-60-90 Triangle Theorem states that in a30-60-90 triangle,Skills Objective C: Calculate lengths of sides in isosceles right triangles and in30-60-90 triangles.In 4–9, find the missing lengths.UCSMP Geometry © Scott, Foresman and Company4. 5.60° 24xx ; y x ; y 6. y7.x6x ; y x ; y 8. 9.50yy8x45° 6 30°10x120°y830°perimeter of square perimeter 205

Name LESSON MASTER 13-5B page 210. A regular octagon’s sides are extended to forma square as shown. Each side of the octagon is3 units long. Find the length of a side of the square.11. How many 30-60-90 triangles can be drawnin a square with 6-cm sides, if the hypotenuseof each triangle is 6 cm? Draw a diagram toshow how you would arrange the triangles.Review Objective F and H, Lessons 13-1 and 13-2In 12–15, tell whether or not the triangles are similar.If so, justify with a similarity theorem.1112. 2713.4825153620252714. 415.128 615 2516. Explain how measuring the shadows DS,cast by yardstick YD, and RE, cast by treeTR , allows you to find the height of the tree.SYDETRUCSMP Geometry © Scott, Foresman and Company17. What measures are needed to find the distancefrom A to B across the lake?COALongLakeD206B

NameL E S S O NM A S T E R13-6BQuestions on SPUR ObjectivesSkillsIn 1–3, use the figure at the right.1. Which side is adjacent to ∠C?A2. Which side is opposite ∠B?3. Which angle is opposite AB?BC4. Trigonometry literally means .Skills Objective D: Determine tangents of angles.5. Consider ABC at the right.a. Give tan B.B12Cb. Give tan A.8c. From tan B, estimate m∠B.d. From tan A, estimate m∠A.ASkills Objective E: Estimate or determine exact values of the tangent ratio.In 6–8, give exact values.UCSMP Geometry © Scott, Foresman and Company6. tan 30° 7. tan 45° 8. tan 60°In 9–14, estimate to the nearest thousandth.9. tan 40° 10. tan 72°11. tan 25° 12. tan 58°13. tan 33.24° 14. tan 16.7°In 15 and 16, use KLM at the right. a. Estimate thetangent of the given angle to the nearest hundredth.b. Determine the measure of the angle.15. a. tan Kb. m∠ KM16. a. tan Mb. m∠ MKL207

Name LESSON MASTER 13-6B page 2Properties Objective G: Know the definition of tangent.17. Use RST at the right. Do not measure.a. Give the tangent of ∠R.RSb.TSis the tangent of which angle?c. How is tan R affected if m∠R increases?RSTSkills Objective I: Use tangents to determine unknown lengths in real situations.18. How tall is Chicago’s 19. How tall is the SanBat Column, aJacinto Monument,sculpture by Claesshown at the right?Oldenburg, picturedat the right?65°45.7' 83° 50'20. How tall is the Leaning 21. How wide is the river below?Tower of Pisa, shownat the right?TomorrowRiver35°86°4.3 m22. The angles of depression to the near and far banks of ariver measure 49 and 11, respectively.a. Draw a picture of this situation.b. If the observer’s eyes are 1.8mabove the ground, how wide is the river?1.8 m49°20 m11°UCSMP Geometry © Scott, Foresman and Companyriver208

NameL E S S O NM A S T E R13-7BQuestions on SPUR ObjectivesSkills Objective D: Determine sines and cosines of angles.1. Use ABC at the right.Ca. Find BC.6b. Find sin B.c. Find sin A.B136Ad. Find cos B. e. Find cos A.f. Estimate m∠B. g. Estimate m∠A.Skills Objective E: Estimate or determine exact values of sine and cosine ratios.In 2–7, give exact values.2. sin 30° 3. sin 45° 4. sin 60°5. cos 30° 6. cos 45° 7. cos 60°In 8–15, estimate to the nearest thousandth.8. sin 40° 9. cos 40°UCSMP Geometry © Scott, Foresman and Company10. cos 65° 11. sin 83°12. sin 47.8° 13. cos 56.1°14. sin 70.5° 15. cos 29.6°In 16–18, use DEF at the right. Do not use a protractor.16. Determine the approximate measure of each angle.a. m∠D b. m∠FD44 mm17. Calculate each sine to the nearest hundredth.Ea. sin D b. sin F58 mm 37 mm18. Calculate each cosine to the nearest hundredth.a. cos D b. cos FF209

Name LESSON MASTER 13-7B page 2Properties Objective G: Know the definitions of sine and cosine.19. Define sin A.In 20–23, use RST at the right.20. Write a ratio for each function.a. sin R b. cos RST21.RSRTis the sine of which angle?22.TSRTis the cosine of which angle?23. How is sin R affected if m∠R increases?RUses Objective I: Use sines and cosines to determine unknown lengths inreal situations.24. From a point at the foot of a hill, the angle of elevationof the top is 15°. The distance from the foot of the hillto the top is 150 meters. Find the height of the hill.25. A 30-foot ladder leans against a building making an angleof 72° with the ground.a. How high on the building does the ladder reach?b. How far from the building is the end of the ladder?26. The tailgate of a tractor-trailer rig is 1 m off the ground.The greatest incline for efficiently loading the truck is 10°.How long should the ramp be for a 10° incline?27. A plane takes off at an angle of 24° with the ground.a. How far has it traveled in a horizontal distanceafter it has traveled 3 miles?b. How high, in feet, is the plane after it has traveled3 miles?UCSMP Geometry © Scott, Foresman and Company28. A biker pedaled up a slope of 6° for 150 meters andthen another 100 meters at a slope of 9°.210a. How far did the biker travel in a horizontal distance?b. How far did the biker climb vertically?

NameL E S S O NM A S T E R13-8BQuestions on SPUR ObjectivesSkills Objective D: Use the SAS area formula.In 1–4, find the area of the triangle.1. 4.52.75°31.32.295°55°3. 4.15.220° 40°1011 1288°5. Find the area of a regular pentagon with sides8 centimeters long.6. Find the area of a regular decagon with sides8 centimeters long.Uses Objective J: Determine components of vectors in real situations.UCSMP Geometry © Scott, Foresman and Company7. A hurricane is moving 30 mph ina direction 23 west of north. Findthe components of its velocity.8. An oil tanker traveled 32 knots(nautical miles) per hour on a course38 north of west. Find thecomponents of its velocity.9. The Fox River flows at a rate of5 kilometers per hour in a direction80 south of east. Find componentsof the river’s velocity.10. A helicopter pilot wants to reach a point 3 km southand 6 km east of the takeoff location.a. In which direction should the helicopter take off?b. How far will the helicopter travel?211

Name LESSON MASTER 13-8B page 211. A sailboat traveled 45 miles on a course 35 north of eastand then traveled 60 miles on a course 75 north of eastbefore the wind died down. Find the actual distance fromits starting point that the boat lost its wind power.Review Objectives D and I, Lesson 13-6 and 13-7In 12–14, use FGH at the right.12. Find each trigonometric ratio.Fa. tan F b. sin Hc. cos H d. sin F13. How are sin H and cos F related?14. How is cos F affected if m∠F increases?GH15. The string of a kite forms an angle of 68 with the ground.If 250 m of string have been let out, how high is the kite?16. A mine shaft forms a 15 angle with the ground and reachesa point 150 feet below the surface. How long is the shaft?17. If the sun’s rays make an angle of 70 with the ground, howlong is the shadow of a person who is 180 cm tall?18. From the top of a 100-foot lookout tower, a forest rangerspotted a fire at a 25 angle of depression. How far wasthe fire from the base of the lookout tower?19. The angle of elevation from an observer on the roof of theGrande Hotel to the roof of the Rio Stock Exchange is a10 angle. The buildings are 300 meters apart. How muchtaller is the Rio Stock Exchange than the Grande Hotel?20. A 90-foot escalator makes an angle of 18 with the lowerlevel of a parking garage. How high does the escalatorrise vertically?UCSMP Geometry © Scott, Foresman and Company21. A ladder mounted on a fire truck is 6 ft above the ground.If the maximum length of the ladder is 120 ft and themeasure of the largest safe angle the ladder can makewith the truck is 75, how high will the ladder reach?212