GEOMETRY L FINAL REVIEW INFORMATIONAL PACKET UNIT OBJECTIVES

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1 GEOMETRYL1 2014FINALREVIEWINFORMATIONALPACKET UNITOBJECTIVES UNIT1 BASICSOFGEOMETRY 1.Identifyandapplythethreeundefinedterms;points,linesandplanes. 2.Usetheundefinedtermstodefinesegments,angles,rays,bisector. 3.Nameandclassifyanglesasacute,right,obtuse. 4.Identifyanglepairsandfindmeasures;adjacent,vertical,supplementary,complementaryusing algebraic(linear,quadratic)methods 5.Applyformulasforperimeter,areaandcircumference. 6.Developandapplytheformulaformidpoint. 7.UsethedistanceformulaandPythagoreanTheoremtofindthedistancebetweentwopointsona coordinateplane. 8.Identifyreflections,rotationsandtranslationsofpoints,lines,segmentsandangles. UNIT2 REASONING&PROOF 1.Useinductivereasoningtoidentifypatternsandmakeconjectures. 2.Findcounterexamplestodisproveconjectures. 3.Identify,writeandanalyzethetruthvalueofconditionalstatementsconverse,inverseand contrapositiveofconditionalstatements. 4.Writeananalyzebiconditionalstatements. 5.Identifypropertiesofequalityandcongruenceandusethemtowritealgebraicproofsand geometricproofs. 6.Writetwocolumnproofs. 7.Provegeometrictheoremsbyusingdeductivereasoning. UNIT3 PARALLEL&PERPENDICULARLINES 1.Identifyparallel,perpendicularandskewlines. 2.Constructparallel,perpendicularandskewlines. 3.Proveandapplytheoremsaboutperpendicularlines. 4.Identifytheanglesformedbytwolinesandatransversal. 5.Proveandusetheoremsabouttheanglesformedbyparallellinesandatransversal. 6.Usetheanglesformedbyatransversaltoprove2linesparallel. 7.Useslopetoidentifyparallelandperpendicularlines. 8.Writeequationsofparallelandperpendicularlines. 9.Classifylinesasparallel,intersectingorcoincidingoncoordinateplane.

2 UNIT4 CONGRUENTTRIANGLES 1.Classifyingtrianglesbyanglemeasureandsideslength. 2.Usetriangleclassificationtofindanglemeasureandsidelength.(Includelinearandquadratic expressions) 3.Usepropertiesofcongruenttriangles. 4.Provetrianglescongruentbyusingthedefinitionofcongruence. 5.ApplySSS,SASandASAtosolveproblemsandprovetrianglescongruent. 6.UseCPCTCtoprovepartsoftrianglescongruent. 7.Draw,identifyanddescribetransformationsoftrianglesinacoordinateplane. 8.Usepropertiesofrigidmotionstodeterminewhetherfiguresarecongruentandtoprovefigures congruent. 9.Positionfiguresincoordinateplaneforuseincoordinateproofs. 10.Provegeometricconceptsbyusingcoordinateproof. 11.Provetheoremsandapplypropertiesaboutisoscelesandequilateraltriangles. UNIT5 PROPERTIESOFTRIANGLES 1.Proveandapplytheoremsaboutperpendicularbisectorsandanglebisectors. 2.Proveandapplypropertiesofperpendicularbisectors,anglebisectors,medians,altitudesand midsegements. 3.Constructaperpendicularbisectorofasegment,ananglebisector,thecircumcenterandincenter ofatriangle. 4.UsetheConverseofPythagoreanTheoremtoclassifytriangles. 5.Justifyandapplypropertiesof454590and306090righttriangles. UNIT6 QUADRILATERALS 1.Findandusethemeasuresofinteriorandexterioranglesofpolygons. 2.Proveandapplypropertiesofparallelograms. 3.Useandapplypropertiesofparallelogramstosolveproblems. 4.Provethatagivenquadrilateralisaparallelogram. 5.Proveanapplypropertiesofrhombi,rectanglesandsquares. 6.Useandapplypropertiesofrhombi,rectanglesandsquarestosolveproblems. 7.Provethatagivenquadrilateralisarhombus,rectangleorasquare. 8.Reflect,rotateandtranslateaparallelogram. UNIT7 SIMILARITY 1.Identifysimilarpolygons. 2.Applypropertiesofsimilarpolygonstosolveproblems. 3.Drawanddescribesimilaritytransformationsinthecoordinateplane. 4.Usepropertiesofsimilaritytransformationstodeterminewhetherpolygonsaresimilarandto provecirclesaresimilar. 5.UseAA,SSSandSASsimilaritycriteriatodetermineiftwotrianglesaresimilar. 6.Usepropertiesofsimilartrianglestosolveproblemsandfindsegmentlengthsbyindirectmeasure. 7.UsepropertiesofsimilartrianglestoapplyTriangleAngleBisectorTheoremandTriangle ProportionalityTheorem. 8.Applysimilartrianglepropertiestousedilationoncoordinateplane.

3 UNIT8 RIGHTTRIANGLES 1.UseGeometricMeantofindsegmentlengthsinrighttriangles. 2.Applysimilarityrelationshipsinrighttrianglestosolveproblems. 3.Findthesine,cosineandtangentofanacuteangle. 4.Usetrigonometricratiostofindsidelengthsandanglemeasuresinrighttrianglesandtosolvereal worldproblemsincludingbutnotlimitedtoangleofelevation,andofdepression,height,distance away,etc. UNIT9 AREA 1.Usetheareaformulaforatriangletocreatetheareaformulaforregularpolygons. 2.Userighttrianglerelationshipstohelpfindtheareaofregularpolygons. 3.Findthemeasureofaremoteinteriorangleofaregularpolygon. 4.Findthesumoftheexterioranglesofaregularpolygon. 5.CalculateGeometricProbability. UNIT10 CIRCLES 1.Identifytangents,secantsandchordsandusetheirpropertiestosolveproblems. 2.Applypropertiesofarcsandchords. 3.Findtheareaofsectors. 4.Findarclengths. 5.Findthemeasureofaninscribedangleandusetheirpropertiesofsolveproblems. 6.Findthemeasuresofanglesandlengthsofsegmentsformedbylinesthatintersectcircles. 7.Usethemeasuresofanglesandlengthsofsegmentsformedbylinesthatintersectcirclestosolve problems. 8.Writeandgraphtheequationofacircle. 9.Usetheequationofacircletosolveproblems. UNIT11 3DIMENSIONALFIGURES 1.Classify3dimensionalfiguresaccordingtotheirproperties. 2.Usenetsandcrosssectionstoanalyze3dimensionalfigures. 3.Applytheformulaforvolumeforprism,cylinder,pyramid,coneandsphere. 4.Usevolumeformulatosolverealworldproblems.

4 GEOMETRYL1 2014FINALREVIEWINFORMATIONALPACKET UNITVOCABULARY UNIT1 BASICSOFGEOMETRY Undefinedterms,point,line,plane,segment,ray,collinear,coplanar,intersect,distance,postulates, congruent,angle,sides,vertex,adjacentangles,acute,right,obtuse,midpoint,bisects,verticalangles, linearpair,supplementary,complementary,angle,area,coordinateplane,perimeter,transformation, dialation,isometry,translation,rotation,reflection,endpoint,preimage,image UNIT2 REASONING&PROOF Conjecture,counterexample,deductivereasoning,inductivereasoning,proof,theorem,postulate, conditionalstatement,biconditionalstatement,conclusion,twocolumnproof UNIT3 PARALLEL&PERPENDICULARLINES ParallelLines,SkewLines,ParallelLines,PerpendicularLines,Transversal,alternateexteriorangles, alternateinteriorangles,correspondingangles,samesideinteriorangles(consecutiveinterior angles),coordinateplane,coordinates,slope,yintercept UNIT4 CONGRUENTTRIANGLES Acutetriangle,obtusetriangle,congruent,equilateraltriangle,interiorangle,exteriorangle,isosceles triangle,righttriangle,scalenetriangle,correspondingangles,correspondingsides,baseangles, vertexangle,bases,hypotenuse,legs,sss,sas,asa,aas,hl UNIT5 PROPERTIESOFTRIANGLES Altitude,perpendicularbisector,median,midsegment,anglebisector,concurrent,equidistant, orthocenter,centroid,incenter,circumcenter,pointofconcurrency UNIT6 QUADRILATERALS Quadrilateral,parallelogram,kite,square,rectangle,polygon,trapezoid,isoscelestrapezoid, rhombus,exteriorangle,equidistant,diagonals,oppositeangles,oppositesides,consecutiveangles, consecutivesides,concave,convex,regular UNIT7 SIMILARITY AASimilarity,correspondingangle,triangleproportionalitytheorem,ratio,proportion,similarity, dilation. UNIT8 RIGHTTRIANGLES Sine,cosine,tangent,SOHCAHTOA,hypotenuse,leg,rightangle,geometricmean,altitude,angleof elevation,angleofdepression,trigratio,inversefunctions,pythagoreantheorem

5 UNIT9 AREA Regularpolygon,interiorangle,exteriorangle,apothem,radius,compositefigure,geometric probability,perimeter,area,pentagon,hexagon,octagon,nonagon,decagon,ngon UNIT10 CIRCLES Radius,diameter,chord,secant,tangent,centralangle,inscribedangle,arc,majorarc,minorarc, semicircle,concentriccircles,exteriorofacircle,interiorofacircle,onthecircle,pointoftangency, sector,arclength,interceptedarc UNIT11 3DIMENSIONALFIGURES Surfacearea,volume,cone,pyramid,prism,sphere,cylinder,polyhedron,radius,greatcircle, hemisphere,cube,edge,vertex

6 Name Date Class Extending Perimeter, Circumference, and Area Chapter Test Form C 1. Express the area of an equilateral triangle in terms of the length s of a side. _ 2. Find the area of the parallelogram. 6. The area of an equilateral triangle is equal to the area of a trapezoid. The trapezoid has bases with lengths 4 centimeters and 14 centimeters and an altitude of 4 3 centimeters. Determine the perimeter of the triangle. _ 3. The longer diagonal of a rhombus is equal to 3 times one of its sides. The length of a side is 6 inches. Determine the area of the rhombus. Leave your answer in simplest radical form. _ 4. The midsegment of the trapezoid has a length of 11.5 cm. Find the area of the trapezoid. 7. A circle is circumscribed about a square. The square has side lengths of 8 inches. Find the circumference of the circle in terms of. Leave your answer in simplest radical form. 8. A regular hexagon is circumscribed about a circle. The circle has a radius of 9 feet. Find the area of the hexagon to the nearest tenth. 9. Find the area of the square. _ 5. Find the area of the kite. _

7 Name Date Class Extending Perimeter, Circumference, and Area Chapter Test Form C continued 10.The radius of the circle circumscribed around the regular hexagon is 10 centimeters. Find the area of the shaded part of the figure to the nearest tenth. 14. Find the area of the polygon with vertices D(4, 1), E(2, 4), F(3, 2), and G(0, 4). 15. Determine the effect on the area of a parallelogram if the height is multiplied by 3 and the base is multiplied by 6. _ 11. Sod is going to be placed over an irregularly shaped area. If sod costs $6 a square yard, estimate the cost of the sod needed to cover the area. The grid has squares with side lengths of 2 feet. 16. A circle has a diameter of 5 feet. If the circumference is multiplied by (2x 4), find the area of the new circle. 17. A point is chosen randomly on AD. Find the probability the point is on BC or CD. _ 12. Find the perimeter of the polygon with vertices A(2, 3), B(1, 5), C(1, 0), and D(2, 2). Round your answer to the nearest tenth. 18. A weather channel covers local weather 6 times per hour for a period of 2 minutes. If you turn to the weather channel 5 times, predict how often you will catch the local weather. _ 13. Find the area of a circle centered at (1, 1) that passes through the point (2, 6). Round your answer to the nearest tenth. _

8 Name Date Class Circles Chapter Test Form C 1. Classify the lines and segments that intersect A. 4. Write True or False. Chords equally distant from the center of a circle are congruent. 5. Find the area of the segment of the circle to the nearest hundredth. 2. Mount McKinley in Alaska is North America s highest mountain. The distance from the summit to the horizon is about 176 miles. To the nearest tenth of a mile, find the height of the mountain. 6. To the nearest degree, find the measure of the central angle for JK if the length of JK is 2.4 units and the radius is 6 units. 7. Find mlpo. _ 3. Given mwvx 45 and VW UX, find m UV. 8. Find mrsp. _

9 Name Date Class Circles Chapter Test Form C continued 9.If macg 65, magc 80, mdc 100, mbc 70, and FA and GC are tangent to the circle, find mafd. 13. Find the length of BD. 14. Find the diameter. _ 10. Find mtmu. 15. Write an equation for the locus of all points in the coordinate plane that are 5 units from (3, 4). _ 11. Find m. SPQ 16. Graph a circle with a diameter of 4 units that is tangent to the line y 2. _ 12. Find the length of KL. 17. A hospital trauma center is going to be built equidistant from three cities. Positioned on a grid, the cities would be located at (3, 2), (2, 3), and (6, 5). What are the coordinates of the location where the trauma center should be built? _

10 Name Date Class Polygons and Quadrilaterals Chapter Test Form C 1. Identify the figure as specifically as possible. 7. Prove that JKLM is a parallelogram. _ 2. An interior angle of a regular convex polygon measures 144. How many sides does the polygon have? _ 3. The exterior angles of a convex pentagon measure (18x 12), 16x, (8x 6), (10x 12), and (5x 12). Determine the measure of the largest interior angle. _ 4. Three vertices of parallelogram PQRS are P(1, 3), Q(4, 1), and R(1, 2). Find the coordinates of vertex S. _ 5. Given ABCD, determine the value of y. 8. Use the definition of parallelogram to show that the quadrilateral with vertices A(4, 4), B(2, 0), C(6, 4), and D(4, 8) is a parallelogram. _ 6. In EFGH, the diagonals intersect at Y. If EY x 2 and GY 2x 3, determine the length of EG. 9. Give the best name for the quadrilateral with vertices (2, 1), (3, 2), (4, 1), and (3, 4). _

11 Name Date Class Polygons and Quadrilaterals Chapter Test Form C continued 10.Find the perimeter of a square if half of a diagonal is equal to 8 inches. _ 14. Give the best name for the quadrilateral with vertices (1, 1), (1, 3), (3, 1), and (1, 3). 11. Determine the value of x. 15. Find the value of x so that ABCD is an isosceles trapezoid with bases AD and BC. _ 12. Write True or False. If the midpoints of the sides of a parallelogram, when connected in order, form a rectangle, then the parallelogram is a rhombus. _ 16. XY is the midsegment of the trapezoid. Find the value of x. 13. Use the diagonals to determine whether a parallelogram with vertices (3, 2), (1, 4), (8, 5), and (6, 7) is a rectangle, rhombus, or square. _

12 Name Date Class Right Triangles and Trigonometry Chapter Test Form C 1. Find x, y, and z. 5. Find the perimeter and area of the triangle. Round to the nearest tenth. _ 2. A photographer positions a camera on a tripod to take a picture of a grain silo. The lens of the camera is 4 feet 6 inches from the ground. To get the full height of the silo, the camera had to be positioned 18 feet from the base of the silo. How tall is the grain silo? 6. Find YZ. Round to the nearest unit. _ 3. Determine the value of cosb to the nearest hundredth. 7. Find md to the nearest degree. _ 4. Complete the chart sin 8. The length of a slide at a water park is 50 feet from the top of the slide to ground level. The top of the slide is 20 feet above the ground. What is the approximate measure of the angle formed by the top of the slide and the vertical support to the ground? Round to the nearest degree. cos tan

13 Name Date Class Right Triangles and Trigonometry Chapter Test Form C continued 9.A plane is flying at a constant altitude of 30,000 feet and a constant speed of 750 miles per hour. A fisher on a lake spots the plane headed in his direction at an angle of elevation of 68. To the nearest minute, now much time will pass before the plane is directly over the fisher? 13. Identify another vector that is parallel to but NOT equal to the resultant vector of 2, 7 3, Find the direction of 6, 4. Round to the nearest degree. _ 10. A forest ranger in a 140-foot-tall observation tower sees a fire moving in a direct path toward a lake. The angle of depression to the fire is 38. The angle of depression to the lake is 88. To the nearest foot, how close is the fire to the lake? _ 11. Find the perimeter of ABC to the nearest tenth. 15. A skiff leaves a dock and heads toward a house across the river. The house is at a bearing of N 648 E from the dock. There is a 1 mile per hour current blowing due east. Determine the speed and direction the skiff would have to maintain so that the skiff s actual speed is 4 miles per hour and it is moving directly toward the house. Round the speed to the nearest whole number and the direction to the nearest degree. _ 12. The coordinates of the vertices of JKL are J(1, 4), K(2, 2), and L(4, 0). Find the measure of the smallest angle of the triangle. Round to the nearest degree. _

14 Name Date Class Spatial Reasoning Chapter Test Form A 1. Classify the figure. 5. Find the volume of the pyramid. _ 2. Describe the three-dimensional figure that can be made from the net. 6. Find the volume of the cone in terms of. _ 3. Find the volume of the cube. Use the figure for Exercises 7 and 8. _ 4. Find the volume of the cylinder in terms of. 7. Find the volume of the sphere in terms of. 8. Find the surface area of the sphere in terms of. _

15 Name Date Class Spatial Reasoning Chapter Test Form B 1. How would you classify a threedimensional figure that has a circular base and a vertex? 6. Find the volume of the cone. Round to the nearest tenth. _ 2. Describe the three-dimensional figure that can be made from the net. 7. Determine the volume of a sphere with a great circle that has an area of 9 cm 2. Give the answer in terms of. _ 3. Find the volume of the regular hexagonal prism. If necessary, round to the nearest tenth. 8. Determine the surface area of a sphere if the diameter is 3 feet. Round to the nearest tenth. _ 4. Find the volume of a cylinder with a base area of 49 in 2 and a height equal to twice the radius. If necessary, round to the nearest tenth. _ 5. Find the volume of a rectangular pyramid with length 5 meters, width 3.4 meters, and height 8 meters. Round to the nearest tenth. _

16 Name Date Class Spatial Reasoning Chapter Test Form C 1.Describe the faces and base(s) of a pentagonal prism. _ 2. Describe the cross section formed by the intersection of a triangular pyramid and a plane parallel to the base of the pyramid. _ 3. Three inches around both ends of the box will be cut and folded to form the top and bottom. Determine the volume of the box. If necessary, round to the nearest tenth. 5. A square pyramid has a slant height of 17 centimeters and a lateral area of 544 square centimeters. Determine the volume of the pyramid. 6. There is a cone-shaped plug in the bottom of a cone. If the height of the plug is 5 inches and the height of the cone is 16 inches, determine the volume of the cone. If necessary, round to the nearest tenth. _ 4. To the nearest cubic centimeter, determine the volume of packing peanuts needed to fill the box if the radius of the enclosed cylinder is 4 centimeters and the cylinder is centered in the box. 7. Determine the diameter of a sphere with a volume of 972 in Find the surface area in terms of of a sphere with a volume of 288 cm 3. _

17 Name Date Class End-of-Course Test Choose the best answer. 1. P is between J and K. The distance between J and P is 7 more than 3 times the distance between P and K. If JK 55, what is PK? A 12 C 24 B 16 D QX bisects PQR. What is the greatest possible whole-number measure of PQX? F 458 H908 G 898 J The ratio of the measures of two supplementary angles is 8 : 4. What is the measure of the smaller angle? A 12 C 60 B 40 D What is the distance between the points (4, -1) and (-2, 3)? F 2 5 H 2 13 G 10 J Which is next in the sequence? 1, 2, 7, 14, 23,... A 24 C 32 B 25 D Which is the converse of the statement? If 6 3x 7, then 3x 1. F If 6 3x 7, then 3x 1. G If 3x 1, then 6 3x 7. H If 6 3x 7, then 3x 1. J If 3x 1, then 6 3x Which conjecture is valid by the Law of Syllogism? Given: If it is June 12, then the local orchestra will play a concert. If the local orchestra is playing a concert in June, then the day must be Tuesday. A If it is June 12, then the day must be Tuesday. B If the local orchestra is playing a concert, then it must be June 12. C If the local orchestra is playing a concert, then it must be a Tuesday in June. D If it is a Tuesday in June, then the local orchestra is playing a concert. 8. In the figure, why is QS QS? F All altitudes are congruent. G Symmetric Property of Congruence H Reflexive Property of Congruence J Transitive Property of Congruence 9. Which names a pair of corresponding angles? A 1 and 6 B 3 and 8 C 2 and 7 D 3 and What is the value of 12x 20? F 34 H 90 G 88 J

18 Name Date Class End-of-Course Test 11. What is the slope of the line that passes through the points (1, 9) and (4, 6)? A 5 3 C 1 5 The figure represents the wooden truss used to support the roof of a garage. Use the figure for Exercises 18 and 19. B 3 5 D Which is the equation of the line in the graph? F y 2x 3 3 G y x 3 2 H y 3x 1 2 J y x Two of the three angle measures in a triangle are given. Which are angle measures of an acute triangle? A 11, 79 C11, 89 B 11, 59 D11, Which polygon has line symmetry but not rotational symmetry? F rectangle H rhombus G square J kite 15. Which are the lengths of the sides of an obtuse triangle? A 8, 11, 15 C 11, 11, 15 B 9, 12, 15 D 10, 12, What is the altitude of an equilateral triangle whose sides measure 42 centimeters? F 21 H 21 3 G 42 J What is the measure of one exterior angle of a regular polygon having 40 sides? A 4.5 C 85.5 B 9 D What postulate or theorem can be used to prove JKM LKM? F SSS H ASA G SAS J HL 19. Given that ML 12 feet, how wide is the garage? A 12 ft C 25 ft B 24 ft D 26 ft 20. What is MP? F 3 2 H 6 G 4 2 J What is the value of x? A 25 C 65 B 29 D Which CANNOT be used to prove that a quadrilateral is a parallelogram? F One pair of opposite angles is congruent. G Both pairs of opposite sides are parallel. H Both pairs of opposite sides are congruent. J One pair of opposite sides is both parallel and congruent.

19 Name Date Class End-of-Course Test 23. The figure represents a rectangular gate with diagonal braces. To the nearest tenth, what is the width, QT, of the gate? A 3.9 ft B 4.9 ft C 7.0 ft D 7.6 ft Refer to the figure for Exercises 24 and Kim is making a kite with a wooden frame. The measures of the frame are shown. She will use cloth binding to cover the outer edges of the kite. To the nearest tenth, how many centimeters of binding will she need? F 58.1 cm H cm G 82.1 cm J cm 25. What is the area of the kite? A 200 cm 2 C 1400 cm 2 B 400 cm 2 D 2800 cm To the nearest tenth, what is AP? F 1.0 m G 2.2 m H 2.5 m J 4.7 m 27. TUV undergoes the dilation: (x, y) (2x, 2y). Then it is translated: (x, y) (x 10, y 8). If vertex T was at (8, 6), what are its coordinates after these two transformations? A (16, 12) C (6, 4) B ( 2, 2) D ( 4, 4) 28. Starla is 5 feet 9 inches tall. To find the height of a tree, she measured her shadow and the tree s shadow. Her shadow was 8 feet long when the tree s shadow was 30 feet long. To the nearest foot, how tall is the tree? F 15 ft H 28 ft G 22 ft J 42 ft 29. MN with endpoints M(9, 3) and N(1, 5) is dilated by a scale factor of 2.5. To the nearest tenth, what is the length of MN? A 16.1 C 25.5 B 17.9 D To the nearest thousandth, what is tan77? F H G J The legs of a right triangle measure 11.4 meters and 15.1 meters. To the nearest tenth, which could be the measure of the smallest angle? A 31.1 C 38.6 B 37.1 D When the angle of elevation to the sun is 26 a flagpole casts a shadow that is 82 feet long. What is the height of the flagpole to the nearest foot? F 36 ft H 74 ft G 40 ft J 166 ft 33. The sides of a triangle measure 18 inches, 25 inches, and 36 inches. To the nearest degree, what is the measure of the largest angle? A 1138 C 1578 B 1478 D 1598

20 Name Date Class End-of-Course Test 34. XYZ is reflected across the line y x. If vertex Z is at (15, 21), where is Z after the reflection? F (15, 21) H (21, 15) G (15, 21) G (21, 15) 35. MN with endpoints M(6, 10) and N(1, 0) is reflected over the y-axis, then translated right 5 units, and down 2 units. What is the coordinate of N ''? A (4, 2) C ( 4, 2) B (4,2) D ( 6, 2) 36. To the nearest tenth, what is the area of a regular octagon with a perimeter of 32 meters? F 77.3 m 2 H m 2 G m 2 J 1024 m The area of a trapezoid is 128 square feet. If the height of the trapezoid is increased by a factor of 5, what is the area of the new trapezoid? A 133 ft 2 C 640 ft 2 B 138 ft 2 D 3200 ft A rectangular scarf with the design shown is set out to dry. A fly lands on the scarf. What is the probability that it lands in the shaded region? F 0.25 H 0.75 G 0.50 J The air conditioner cycles on once every 28 minutes and stays on for 7 minutes. Find the probability that the air conditioner will be on when you walk in the door. A 0.2 C 4 B 0.25 D 5 40.What is the volume of a rectangular prism that is 4 inches wide, 9 inches long, and 3 inches high? F 36 cm 3 H 324 cm 3 G 108 cm 3 J 432 cm To the nearest tenth, what is the volume of a cylinder with a diameter of 22 centimeters and a height of 13 centimeters? A cm 3 C cm 3 B cm 3 D 19,766.9 cm What is the volume of a square pyramid with base area of 4 square meters and a height of 6 meters? F 6 m 3 H 12 m 3 G 8 m 3 J 24 m To the nearest tenth, what is the area of a sector of a circle of radius of 9 meters if the central angle is 50? A 1.3 m 2 C 35.3 m 2 B 5.1 m 2 D 70.7 m 2 Refer to the figure for Exercises 44 and mpn 78, mqn 163.5, and mmq 72. What is mprm? F 47 H94 G 57 J PR 6, NR 15, and QR 14. To the nearest tenth, what is MR? A 5.6 C 6.4 B 6.0 D The equation for a circle is (x 4) 2 (y 3) Which pair of coordinates locates its center? F (4, 3) H (16, 9) G (4, 3) J (16, 9) 241

21 Name Date Class Cumulative Test B Choose the best answer. 1. P, W, and K are collinear, and W is between P and K. PW 10x, WK 2x 7, and PW WK 6x 11. What is PK? A 25 C 90 B 65 D RM bisects VRQ. If mmrq 828, what is mvrm? F 41 H 98 G 82 J The measure of the complement of an angle is 59. What is the measure of the supplement of the angle? A 31 C 121 B 39 D What is the midpoint of the segment whose endpoints are (17, 1) and (9, 3)? F (8, 4) H (13, 1) G (4, 2) J (26, 2) 5. To the nearest tenth, what is the distance between the points (12, 9) and (6, 10)? A 16.3 C 19.9 B 18.0 D Which is the image of (4, 7) rotated 180 about the origin? F (4, 7) H (4, 7) G (7, 4) J (7, 4) 7. What is the next letter in the series? a b d g k p... A q C v B u D z 8. If 7k 12 and 6c 7k, which is true by the Transitive Property of Equality? 9. Which statement has a true converse? A If exactly two angles of a triangle are acute, then the triangle is an acute triangle. B If two angles of a triangle are congruent, then the sides opposite them are congruent. C If the sum of two angles of a triangle is more than 90, then one of the two angles is obtuse. D If no two angles of a triangle are congruent, then the triangle is not scalene. 10. Given: If two angles of a triangle are congruent, then the triangle is isosceles. If a triangle is isosceles, then two altitudes of the triangle are congruent. Which conjecture is valid by the Law of Syllogism? F If two angles of a triangle are congruent, then the triangle is isosceles. G If two altitudes of a triangle are congruent, then the triangle is isosceles. H If two angles of a triangle are congruent, then two altitudes of the triangle are congruent. J If two altitudes of a triangle are congruent, then the base angles of the triangle are congruent. 11. Which biconditional statement is false? A x 1 if and only if x 2 1. B Three points are collinear if and only if one point is between the other two. C An angle is a straight angle if and only if its sides are opposite rays. D A polygon is a triangle if and only if it has exactly three sides. F c 2 H 7k 7k G 7k 6c J 6c 12

22 Name Date Class Cumulative Test B continued 12. Which statement is true? F r s H q s G q r J p q 13. What is the slope of the line that passes through (11, 7) and (3, 8)? A 8 C B 1 D What is the slope of a line parallel to a line whose slope is 5 2? 18. One angle of an obtuse triangle measures 168. Which could be another angle measure of the triangle? F 898 H 748 G 808 J The sum of the measures of two angles of a triangle is 90. Which type of triangle is it? A right C equilateral B obtuse D acute 20. A base angle of an isosceles triangle measures 32. What is the measure of the exterior angle at the vertex? F 16 H 64 G 32 J Which CANNOT be used to justify the statement PQR TUV? F 5 2 H 2 5 G 2 5 J Which is an equation of the line in the graph? A y x C y 2 3 x 2 B y x D y 2 x The graph of which equation intersects the graph of y 5x 6 in one point? F y 5 5(x 1) G 5x y 3 H 10x 2y 3 J y 5 5(x 1) 17. Which segment lengths are the lengths of the sides of a scalene triangle? A 7, 7, 7 C 2, 3, 3 B 4, 5, 8 D 5, 5, 6 A SSS C AAS B SAS D ASA 22. A base angle of an isosceles triangle measures (3x 9). The vertex angle measures 12x. What is the measure of the vertex angle? F 12 H 132 G 108 J What is the value of x? A 3 B 6 C 7.5 D 10.5

23 Name Date Class Cumulative Test B continued 24. In RST, ms 49 and mt 52 Which list shows the side lengths from least to greatest? 31. In WXYZ, find mw. F ST, RT, RS H RT, RS, ST G ST, RS, RT J RT, ST, RS 25. Which inequality MUST be true? A a d C b c B c b D a d 26. Which segment measures could be the lengths of the sides of an acute triangle? F 10, 15, 16 H 11, 5 6,18 G 10, 12, 2 61 J 11, 60, The hypotenuse of a triangle measures 10 3 inches. What is the measure of the longer leg? A 5 in. C 10 in. A 878 C 918 B 898 D One diagonal of a square divides the other into two segments measuring 8 2 and 2y. What is the perimeter of the square? F y H 32 2y 2 G 32 2y J One of the diagonals of a kite bisects two of the angles into 508 and 448 angles. What is the measure of one of the other angles of the kite? A 48 C 868 B 88 D The figure PQRS is an isosceles trapezoid with PS QR. B 5 3 in. D 15 in. 28. One leg of a triangle measures 12 centimeters. What is the length of the hypotenuse? F 4 3 cm H 12 2 cm G 6 2 cm J 12 3 cm 29. What is the measure of one interior angle of a regular polygon that has 40 sides? A 9 C 140 B 40 D 171 Which statement is NOT true? F PTS QTR G PQT RTS H PSR QRS J PQS QPR 35. In the figure, JMK RMQ. What is JM? 30. The diagonals of a rhombus are congruent. What is the best name for the figure? F parallelogram H rectangle G rhombus J square A 9.6 C 14.4 B 11.2 D 21.6

24 Name Date Class Cumulative Test B continued 36. Raoul uses tongs to adjust logs in his fireplace. He opens the handles of the tongs 16 inches to move a log. To the nearest inch, how wide is the log? F 6 in. H 10 in. G 7 in. J 36 in. 37. Drake wants to reduce an 8-inch by 10-inch photo so that the width is 5 inches. What will be the measure of the length? A 4 in. C 7 in. 1 B 6 in. D 16 in What is WY? F 24 H 34 G 30 J The shadow of a 6-foot man is 8 feet. At the same time, how long a shadow would a 90-foot monument cast? 2 A 6 in. C 67 ft 6 in. 5 B 1 ft in. D 120 ft 40. LMN was mapped to triangle XYZ. If LMN is similar to XYZ what could the tranformation have been? F (x, y) (4x, 5y) G (x, y) (2x, 3y) H (x, y) (5x, 4y) J (x, y) (2x, 2y) 41. An altitude divides the hypotenuse of a right triangle into two segments measuring 3.6 and 6.4 centimeters. What is the length of the altitude? A 4.8 cm C 10 cm B 5 cm D cm 42. One angle of a right triangle measures The adjacent leg measures 7 yards. To the nearest tenth of a yard, what is the measure of the hypotenuse? F 3.6 yd H 7.9 yd G 6.2 yd J 15.2 yd 43. To the nearest tenth, the sides of a right triangle measure 56, 33, and 65. To the nearest degree, what is the measure of the smallest angle? A 30 C 32 B 31 D A helicopter pilot sights a landmark at an angle of depression of 22 The altitude of the helicopter is 1450 feet. To the nearest foot, what is the horizontal distance from the helicopter to the landmark? F 543 ft H 3589 ft G 586 ft J 3871 ft 45. Two sides of a triangular field measure 11.1 meters and 13 meters. The included angle measures 98. Find the measure of the third side to the nearest tenth of a meter. A 2.5 m C 18.2 m B 15.9 m D 48.4 m 46. A motorboat heads N 158 W to cross a river flowing 7.25 miles per hour due east. The boat travels at the speed necessary to head due north. To the nearest mile per hour, how fast is the motorboat traveling? F 2 mi/h H 27 mi/h G 8 mi/h J 28 mi/h

25 Name Date Class Cumulative Test A Choose the best answer. 1. An angle measures 42 degrees more than twice the measure of its complement. What is the measure of its complement? A 16 C 46 B 26 D The circumference of a circle is square centimeters. What is the diameter of the circle to the nearest tenth? F 6.5 cm H 21.4 cm G 13.1 cm J 42.9 cm 3. M is the midpoint of AB. M has coordinates (3, 8) and B has coordinates (1, 6). What are the coordinates of point A? A (5, 22) C (1, 20) B (4, 1) D (5, 22) 4. What are the coordinates of the image of (3, 7) after the translation (x, y) (x 9, y 9)? F (6, 16) H (12, 2) G (6, 16) J (12, 2) 5. Which is the next number in the series? 1, 0, 3, 8, 15, 24, 35,... A 46 C 59 B 48 D Which is the converse of the statement? If x 10, then y 4. F If x 10, then y 4. G If y 4, then x 10. H If x 10, then y 4. J If y 4, then x What is sin 49 to the nearest tenth? A 0.7 C 1.2 B 0.8 D Ray wants to prove the following theorem. If two angles are complementary to two congruent angles, then the original two angles are congruent. He draws this diagram. Which is the best given information? F QMR UMT G QMR and RMS are complementary angles. UMT and TMS are complementary angles. H SM QU, and UMT and TMS are complementary angles. J QMR UMT, SM QU 9. What is the value of x? A 80 C 92 B 88 D Which inequality shows all possible solutions for x? F x 6 G x 6 1 H x J x 6 2

26 Name Date Class Cumulative Test A continued 11. What is the slope of the line that passes through (7, 3) and (2, 4)? A 9 C 5 7 B 1 D Which line coincides with the graph of the line 2x 6y 12? F y 2x 2 H y 1 x 2 3 G y 3x 2 J y 1 x What is the classification of PQR according to its angles? A right B obtuse C acute D equiangular 14. What is mk? F 158 G 258 H 458 J Which can be used to prove TUV VWT? A SAS B AAS C ASA D HL 16. What is mr? F 458 G H 638 J If P is the incenter, what is PK? A 3.2 cm B 4.0 cm C 4.2 cm D 4.4 cm 18. What is x? F 1 cm H 1.75 cm G 1.5 cm J 2 cm 19. Which could NOT be the length of the third side of a triangle if two of its sides measure 15 feet and 40 feet? A 20 ft C 40 ft B 30 ft D 50 ft 20. The lengths of the shortest and longest sides of an acute scalene triangle are 9 meters and 41 meters. Which could be the length of the third side? F 39 m H 41 m G 40.5 m J 42 m 21. One exterior angle of a regular polygon measures 248. What is the sum of the measures of the interior angles of the polygon? A 3608 C B 9908 D A city park is in the shape of a parallelogram as shown. Two paths will be installed along the diagonals. What is the total length of the paths? F 6.3 yd H 15.1 yd G 12.6 yd J 17.6 yd

27 Name Date Class Cumulative Test A continued 23. The figure is a rectangle. What is x? A 29 C 61 B 58 D A water slide in the middle of a water park pool has opposite sides in the shape of a trapezoid. Half of the slide is below water level. What is the length of the base of the slide? F 5.7 m H 7 m G 6 m J 7.8 m 25. Point Z in XYZ has coordinates (5, 4). XYZ was dilated by a scale factor of 0.8. Name the coordinates of the image of point V. A (5.8, 3.2) C (4, 3.2) B (5.8, 4.8) D ( 3.2, 4) 26. Two American flags of different dimensions are properly folded into two similar isosceles right triangles. The ratio of the length of the legs of the smaller triangle to that of the larger triangle is 4 : 5. If the length of the hypotenuse of the larger triangle is 2 feet, what is the length of the hypotenuse of the smaller triangle to the nearest tenth of a foot? F 0.1 ft H 1.6 ft G 0.6 ft J 2.5 ft 27. What is ST? 28. A 5 foot 6 inch boy casts an 8-foot shadow at the same time a nearby building casts a 44-foot shadow. To the nearest foot, what is the height of the building? F 30 ft H 1000 ft G 64 ft J 1936 ft 29. What is the magnitude of the vector 7, 4 to the nearest tenth? A 2.4 C 8.1 B 5.7 D The legs of a right triangle measure 14 and 25. To the nearest tenth of a degree, what is the measure of the angle opposite the shortest side? F H G J A forest ranger in a 100-foot observation tower sees a fire. The angle of depression to the fire is 48. To the nearest foot, what is the horizontal distance between the tower and the fire? A 100 ft C 1433 ft B 1430 ft D 1434 ft 32. If 2(x 5) 10, then what justifies the statement x 5 5? F Distributive Property G Associative Property of Equality H Transitive Property of Equality J Division Property of Equality 33. To the nearest tenth, what is the area of the regular hexagon? A cm 2 C cm 2 B cm 2 D cm 2 A 3.6 m B 7.2 m C 9.8 m D 10.8 m

28 Name Date Class Cumulative Test A continued 34. To the nearest tenth, what is the area of the shaded region? F 35.0 cm 2 G 44.0 cm 2 H 51.5 cm 2 J cm What is the area of a square with a diagonal of 16? A 256 C 128 B 16 D A radio station reports news and weather every 20 minutes for 4 minutes. If the radio is turned on at a random time, what is the probability that the news and weather report is NOT on? F 0.2 H 0.6 G 0.4 J The cross section of a three-dimensional figure is a circle. Which figure could it NOT be? A cone C prism B sphere D cylinder 38. The area of a parallelogram is 60 square inches. What is the area of the parallelogram if the base is multiplied by 3 4? 3 2 F 33 in H 80 in 2 4 G 45 in J 106 in The volume of a cylinder is 80 cubic centimeters. If the diameter and height of the cylinder are multiplied by 4, what is 5 the volume of the new cylinder? A cm 3 C cm 3 B cm 3 D cm The radius and height of a cylinder are multiplied by 5. What is the effect on the volume? F The volume is multiplied by 1. 5 G The volume is multiplied by 5. H The volume is multiplied by 25. J The volume is multiplied by To the nearest tenth, what is the area of a sector with a radius of 8 centimeters and a central angle of 45? A 4.5 cm 2 C 50.3 cm 2 B 25.1 cm 2 D cm What is mrst? F 27 G 54 H 76.5 J What is the equation for the graph of the circle? A (x 3) 2 (y 2) 2 6 B (x 3) 2 (y 2) 2 6 C (x 3) 2 (y 2) 2 36 D (x 3) 2 (y 2) What is x? F 8 yd G 16 yd H 20 yd J 32 yd