MATH BLASTER GEOMETRY - Knowledge Adventure
M ATH B LASTERG EOMETR Y T EACHERM ATERIALS0361601 Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.1Math Blaster Geometry
MATH BLASTER GEOMETRY TABLE OF CONTENTSPROGRAM OVERVIEW . . . . . . 5UNIT 3: QUADRILATERALS ANDOTHER POLYGONS . . . . . . . . . . . 26Tree DiagramQuadrilatral RelationshipsConcave or Convex?Cut Out the AnglesAngles of PolygonsINTRODUCTION . . . . . . . . . . . . 6PART 1: GEOMETRY TOPICSUNIT 1: POINTS, LINES, PLANES,AND ANGLES . . . . . . . . . . . . . . . . . 7The Whole TruthName That AngleTrue or False?Label the DiagramFind Your Own AnglesUNIT 4: SIMILARITY . . . . . . . . . . 35Ratio and ProportionExploring SimilaritySimilar PolygonsSpecial Right TrianglesConstructing Similar PolygonsUNIT 2: TRIANGLES . . . . . . . . . . . . 16Characteristics of a TriangleTriangle ApplicationsCongruent TrianglesFind the Fastest RoutePoints of Concurrency Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.UNIT 5: CIRCLES . . . . . . . . . . . . . 45Circle ConstructionMore Circle ConstructionParts of a CircleLabel the CircleApplications with Circles2Math Blaster Geometry
TABLE OF CONTENTSCONTINUEDUNIT 6: PERIMETER AND AREA . . 54UNIT 9: TRANSFORMATIONALGEOMETRY . . . . . . . . . . . . . 83Area of ParallelogramsArea of TrianglesArea of TrapezoidsArea of CirclesRecreation AreaTranslations and RotationsReflectionsTransformationsTranslations and Reflections on aCoordinate PlaneRotations on a Coordinate PlaneUNIT 7: SOLIDS . . . . . . . . . . . . . . 64Characteristics of SolidsSurface Area of SolidsVolumeVolume and Surface Area ApplicationsUNIT 10: REASONING ANDPROOF . . . . . . . . . . . . . . . . 93Logical ReasoningCut-and-Paste ProofsUNIT 8: COORDINATE GEOMETRY . . . 73Distance FormulaMidpoint FormulaQuadrilaterals on Coordinate GridsMore Quadrilaterals on Coordinate GridsEquation of a Line Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.PART 2: BRAIN TEASERS. . . 102GeoboardTangramsGeometry Blaster Game ConnectionsConstructionsWorld Wide Web Sites3Math Blaster Geometry
CONTENT DEVELOPERSPAM HALLORANKATHLEEN S. COLEMANMICHELE LEONETTIALISON BIRCHDESIGN AND LAYOUTLAURIE GALVANPAM WISSINGEREDITORJOE SKELLEYReproduction of these pages by the classroom teacher for use in the classroom is permissible. The reproduction ofany part of this book for an entire school or school system or for commercial use is strictly prohibited Vivendi Universal Publishing and/or its subsidiaries. All Rights Reserved.Math Blaster is a registered trademark of Vivendi Universal Publishing and/or its subsidiaries.All trademarks referenced herein are the property of their respective owners.4Math Blaster Geometry
MATH BLASTER GEOMETRY ACTIVITY COMPONENTSMATH BLASTERGEOMETRY LEVELHigh SchoolFEATURES Animated lessons makegeometry come aliveFollows National Council ofTeachers of Mathematics guidelinesContent connects geometric principles to real-life applicationsFriendly interface enables quickaccess to specific subjects andlevelsOn-screen help and glossary ofgeometry termsRecords and tracks students‘progressThe evil Geometrons are downsizing Zoid’s home planetfrom 3-D to 2-D! Learn geometry principles as you collectpieces to restore the Dimension Machine.Building of Truth – Help Andi and Zoid obtain apiece by classifying geometric figures.Pit of Despair – Adjust your angle to shoot targets toremove the shield covering the puzzle piece.Proof Palace – Rearrange the statements or reasonsand solve the proofs.N-Gon Mountains – Scale the highest peak byanswering multiple-choice questions.Capitol Building – Match up the pairs based on therule that is known.Sphinx – Answer the question to unlock the door to theDimension Machine.Dimension Machine – What would each piece looklike if folded into a cube? Answer this to repair themachine.SKILL DEVELOPMENT Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved. Inductive, deductive, and geometric proofs Attributes of triangles, circles, and quadrilaterals Symbols, formulas, postulates and theorems Similarity with ratios and proportions Area and volume of solids – prisms, pyramids, cones,cylinders and spheres Compass and protractor use Coordinate and transformational geometry5Math Blaster Geometry
INTRODUCTIONDear Colleague,Math Blaster Geometryoffers customizedassessment andindividualizedinstruction thatincrease efficiencyand allow more timefor individualized instruction andplanning.Welcome to Math Blaster Geometry!Our primary goal is to help youteach geometry in a way thatengages your students’ interest,interactively enabling them to understand and appreciate the place ofgeometry in mathematics class, theenvironment, or even a potentialcareer field.We invite your comments and observations. Please send them to us by mailor at our Internet address (http://www.education.com). We lookBy including a full year of geometrytopics, we help streamline yourteaching preparations. The 52 subject areas in the program, combinedwith these print activities, encourageand enable your students to understand and apply geometric conceptsin algebra, trigonometry, and traditional proofs. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.forward to hearing from you.Yours in mathematics education,The Blaster DevelopmentGroup6Math Blaster Geometry
UNIT 1 –POINTS, LINES, PLANES, ANDANGLESLesson 1: The Whole TruthLesson 2: Name That AngleLesson 3: True or False?Lesson 4: Label the DiagramLesson 5: Find Your Own Angles Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.7Math Blaster Geometry
UNIT 1 – POINTS, LINES, PLANES, AND ANGLESLESSON 1: THE WHOLE TRUTHLESSON 4: LABEL THE DIAGRAMHand out copies of the Whole Truth activitysheet, p. 9. This activity includes 15 statementsabout different characteristics of points, lines, andplanes. The information in each statement is eitheralways true, sometimes true, or never true. As students read the statements, they are encouraged toconsider different situations with lines, points, andplanes before writing whether the statement isalways, sometimes, or never true. Once studentshave completed the activity, you may wish to discuss students’ reasons for the answers they wrote.Hand out copies of the Label the Diagramactivity sheet, p. 12. This lesson provides studentsthe opportunity to apply the characteristics ofangles and bisectors by labeling a diagram. Thestatements given lead to conclusions about thelocations of points and the measures of angles.Point out that the steps should be performedsequentially.Instruct students to keep the completed activitysheet. They will need the diagram for the exercises in Lesson 5.LESSON 2: NAME THAT ANGLELESSON 5: FIND YOUR OWNANGLESHand out copies of the Name That Angleactivity sheet, p. 10. To define each of the termson this page, students must understand the characteristics of several kinds of angles, bisectors,and lines. Students then apply the definitions bydrawing an example for each term. Remind students to label their drawings. Some students mayprefer to draw only one or two diagrams whichinclude examples of all the terms.Hand out copies of the Find Your OwnAngles activity sheet, p. 13, and have studentstake out their copies of Lesson 4. In Part A ofthe new lesson, students find examples of differentkinds of lines, angles, and bisectors. This involvesstudying and analyzing all aspects of the diagram. You may find it helpful to review propernotation for angles.LESSON 3: TRUE OR FALSE?In Part B, students are given a pair of anglesand then asked to classify these angles in twodifferent ways. When students explain theiranswers, they clarify their thinking and demonstrate understanding.Hand out copies of the True or False? activitysheet, p. 11. In this activity, students go beyondnaming characteristics and definitions. Each statement describes a situation involving angles, bisectors, or lines that may or may not be true. Youmay want to suggest that students make drawingsto help them decide if a statement is true or false.Students can compare answers and discuss whythe statements can or cannot be true. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.8Math Blaster Geometry
UNIT 1THE WHOLE TRUTHLESSON 1NAMEDirections: Read each statement carefully. Determine if the statement is always true,sometimes true, or never true. Complete each sentence with the appropriate word:always, sometimes, or never.1. A line is labeled by a single lowercase letter.2. If two distinct lines intersect, they intersect at exactlyone point.3. If two planes intersect, they intersect at exactlyone point.4. Two collinear points are coplanar.5. Two coplanar points are collinear.6. Three coplanar points are collinear.7. Three collinear points are coplanar.8. Given two points A and B in a plane, ray AB and ray BA arethe same ray.9. The intersection of a line and a plane is one point.10. A point has size, but has a location.11. A segment is part of a line.12. AB, AB, and AB refer to the same set of points.13. If two segments are coplanar, they intersect ata point.14. A plane extends in three dimensions.15. Two distinct points determine exactly one line. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.9Math Blaster Geometry
UNIT 1NAME THAT ANGLELESSON 2NAMEDirections: Define each term and draw an example.A. Acute angle:B. Obtuse angle:C. Straight angle:D. Adjacent angles:E. Complementary angles:F. Supplementary angles:G. Vertical angles:H. Segment bisector:I. Angle bisector:J. Perpendicular lines: Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.10Math Blaster Geometry
UNIT 1TRUE OR FALSE?LESSON 3NAMEDirections: For each statement, write T (true) or F (false).1. Both angles in a pair of complementary angles can be obtuse.2. Two perpendicular lines create congruent, adjacent angles.3. Two vertical angles always have a common vertex.4. A segment bisector creates two congruent segments.5. Two complementary angles always have a common vertex.6. Two vertical angles can be obtuse.7. Each point on an angle bisector is equidistant from the two sides.8. Both angles in a pair of supplementary angles can be obtuse.9. The angles of a pair of supplementary angles can be acute or obtuse.10. An angle bisector can be a point.11. Two angles complementary to the same angle are congruent to each other.12. Both angles of a pair of supplementary angles can be acute.13. Two perpendicular lines always form four right angles.14. A pair of vertical angles are always congruent.15. By definition, two complementary angles must also be adjacent angles.16. A segment bisector can be a segment, ray, or line.17. By definition, two supplementary angles must also be adjacent angles.18. Together, a pair of adjacent supplementary angles form a straight angle. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.11Math Blaster Geometry
UNIT 1LESSON 4NAMELABEL THE DIAGRAMDirections: Use the information below to complete the diagram. You will label5 points and 4 angle measures.CA30 20 30 B45 DInformationWhat to Draw1. CD bisects AB at point M.1. Label point M.2. The measure of AME is 20 .2. Label point E.3. The measure of BMF is 45 .3. Label point F.4. MF bisects BMD.4. Label the measure of DMF.5. CD is AB.5. Label the 3 missing angle measures.6. AMG and BMH are acute, verticalangles.6. Label points G and H. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.12Math Blaster Geometry
UNIT 1LESSON 5FIND YOUR OWN ANGLESNAMEA. Directions: Refer to your completed diagram in Lesson 4. Use proper notation toidentify an example of each of the following items. There is more than one possibleanswer for many of the items.1.midpoint7.angle bisector2.segment bisector8.straight angle3.acute angle9.obtuse angle4.vertical angles10.adjacent angles5.complementaryangles11.6.right anglesupplementaryangles12.pair of perpendicularlinesB. Directions: Refer to your completed diagram from Lesson 4. Write two differentangle classifications that apply to each item below. On the back, explain youranswers.1. AMC and BMC2. AMG and BMH3. DMF and BMF4. CMG and DMH Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.13Math Blaster Geometry
UNIT 1 – ANSWER KEYLESSON never, alwaysalwaysneversometimesneveralwaysSupplementary angles: two angles whosemeasures have a sum of 180 .G. Vertical angles: two opposite angles formedby intersecting lines.H. Segment bisector: a segment, ray, or line thatdivides a segment into two equal parts.I.Angle bisector: a ray that divides an angleinto two congruent angles.J.Perpendicular lines: two lines that intersect toform right angles.LESSON 2Student drawings will vary.A. Acute angle: an angle whose measure is lessthan 90 .LESSON 31.2.3.4.5.6.7.8.9.B. Obtuse angle: an angle whose measure isgreater than 90 .C. Straight angle: an angle whose measureequals 180 .D. Adjacent angles: two angles in a plane witha common vertex and a common side, but nocommon interior FTE. Complementary angles: two angles whosemeasures have a sum of 90 .LESSON 4CHE60 70 M20 30 A30 45 60 45 BGFD Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.14Math Blaster Geometry
UNIT 1 – ANSWER KEYLESSON 52. AMG and BMH are both acute anglesbecause their measures are less than 90 .They are also vertical angles because theyhave a common vertex and are oppositeangles formed by the intersecting lines HGand AB.Answers may vary. Sample answers are provided.A.1.2.3.4.5.6.7.8.9.10.11.12.MCD EMA GMD and CMH CMH and BMH AMDMF AMB EMH DMG and DMF AMF and BMFCD AB3. DMF and BMF are complementaryangles because the sum of their measuresequals 90 . They are also adjacent anglessince they share a vertex and a side butdon’t share interior points.4. CMG and DMH are vertical angles because they have a common vertex and areopposite angles formed by the intersectinglines CD and GH. Both angles are obtusesince their measures are greater than 90 .B.1. AMC and BMC are right angles, sincethey are formed by two perpendicular lines.They are also adjacent angles because theyshare a vertex and side, but don’t shareinterior points. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.15Math Blaster Geometry
UNIT 2 –TRIANGLESLesson 1: Characteristics of a TriangleLesson 2: Triangle ApplicationsLesson 3: Congruent TrianglesLesson 4: Find the Fastest RouteLesson 5: Points of Concurrency Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.16Math Blaster Geometry
UNIT 2 – TRIANGLELESSON 1: CHARACTERISTICS OF ATRIANGLELESSON 4: FIND THE FASTEST ROUTEHand out copies of the Find the Fastest Routeactivity sheet, p. 21. To complete the activity, students label distances on the map. One missingdistance can be found by subtracting, while theother distance is determined by applying thePythagorean theorem. Once students know all thedistances, they use the travel speeds given todetermine the approximate time it takes to get tothe airport by each route. Some students mightuse proportions to find the answers. If necessary,review concepts related to ratios and proportions.Hand out copies of the Characteristics of aTriangle activity sheet, p. 18. Students should befamiliar with the characteristics of different kindsof triangles. In Part A, they use the informationprovided on the triangle drawings to determine allpossible labels for each figure. Suggest that students study the relationship of the sides of the triangles as well as the angle measures.For Part B, make sure students understand thatthey can draw any triangles that fit the givendescriptions. Tell students that their drawings canbe labeled with angle measures, side measures,congruent symbols, or right angle symbols.You could provide extensions to this problem bychanging the travel times on the roads. You mightchallenge students to write their own problemssimilar to this one.LESSON 2: TRIANGLE APPLICATIONSHand out copies of the Triangle Applicationsactivity sheet, p. 19. You may wish to assign thislesson at or near the end of the unit. Students apply a variety of information from throughout theunit to find the missing measures of the triangles.Allow students to use whatever strategies theywant in order to solve the problems. You may wishto have students compare methods once they havecompleted the activity.LESSON 5: POINTS OF CONCURRENCYHand out copies of the Points of Concurrencyactivity sheet, p. 22. When students explore concepts and make their own discoveries, they arelikely to better understand and remember rules. Inthis activity, students construct angle bisectors andperpendicular bisectors to examine the distancefrom the points of concurrency to parts of the triangle. They measure distances and write theirown rules about the incenter and circumcenter ofa triangle. As a challenge, students can study theorthocenter (intersection of all altitudes) and centroid (intersection of all medians) of triangles tosee if similar rules can be stated.LESSON 3: CONGRUENT TRIANGLESHand out copies of the Congruent Trianglesactivity sheet, p. 20. This activity requires studentsto apply the different congruency theoremspresented in this unit in determining congruenttriangles. Ask students which theorems theyused to solve the problems, and then ask volunteers to present different ways of solving thesame problems. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.17Math Blaster Geometry
UNIT 2LESSON 1CHARACTERISTS OF A TRIANGLENAMEA. Directions: Circle all the words that describe each uilateralobtuse40 30 110 uilateralobtuse534B. Directions: Draw a triangle that fits each description and label the identifyingparts.1. Right Scalene3. Acute Scalene2. Obtuse Isosceles4. Right Isosceles Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.18Math Blaster Geometry
UNIT 2LESSON 2NAMETRIANGLE APPLICATIONSDirections: Solve for the missing measures.B1. What is the measure of BAC ABC?40 110 CA30 DB2. What is the measure of ABE?40 40 A100 ECDA3. DB is a median. What is the measure of AB?B5CD34. Given that AB 10 and DC 6, find the following measures:AAC DB AD CAD B Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.50 50 D19CMath Blaster Geometry
UNIT 2LESSON 3NAMECONGRUENT TRIANGLESDirections: Complete the following 4 steps for each problem:1. Label the figure based on the given information.2. Determine if any two triangles can be proven congruent.3. Write the congruence statement.4. State the theorem that proves the triangles are congruent.1. Given: ACE is isosceles with AC CE;BE and AD are medians.CBD EATheorem:B2. Given: BE AE; AB CD. CTheorem:AED3. Given: ADC is isosceles with AD DC; AEC is isosceles with AE EC;DB is a median.DE ABATheorem:CB4. Given: ABCD is a rectangle. Theorem:C Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.D20Math Blaster Geometry
UNIT 2LESSON 4NAMEFIND THE FASTEST ROUTEDirections: Imagine that you are at your home on the corner of 15th Street andCrosstown Boulevard. You need to get to the airport as quickly as possible. Use themap and the information below to answer the questions. Show your work. Roundnumbers when appropriate.2. The distance from thecorner of 15th Streetand Main Street to theairport is 22 miles. Labelthis distance on the map.AirportCroBlv sstowd.n1. The distance from yourhome down 15th Streetto Main Street is 8 miles.Label this distance onthe map.15th StreetMain StreetHome3. The distance from the intersection of Crosstown Boulevard and Main Street to theairport is 16 miles. Label this distance on the map.4. What is the distance from the intersection of 15th Street and Main Street to the intersection of Crosstown Boulevard and Main Street? Label this distance on the map.5. What is the distance from your home down Crosstown Boulevard to Main Street?Label this distance on the map.6. Traffic on 15th Street is moving at about 45 mph. Traffic on Crosstown Boulevard ismoving at about 40 mph. Traffic on Main Street is moving at about 40 mph.Approximately how long will it take to get from your home to the airport using the twodifferent routes? Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.21Math Blaster Geometry
UNIT 2LESSON 5POINTS OF CONCURRENCYNAMEConcurrent lines are two or more lines that intersect at the same point. Thepoint of concurrency is the point at which two or more lines intersect. Triangleshave special points of concurrency which can occur either inside or outside of atriangle.Directions: Construct the points of concurrency based on the information below.Label each point with a letter. Then describe a special characteristic of each point.ABTriangle 1ACBCTriangle 21. The incenter of a triangle is the point at which all the angle bisectors of the triangleintersect. Construct the incenter of Triangle 1 above. Label this point X.2. Measure the distance from the point of concurrency to the three sides.X to BC X to AC X to AB 3. In your own words, what is a special characteristic of the incenter of a circle?4. The circumcenter of a triangle is the point at which all the perpendicular bisectorsof the sides of a triangle intersect. Construct the circumcenter of Triangle 2. Label thispoint Y.5. Measure the distance from the point of concurrency to the three vertices.AY BY CY 6. In your own words, what is a special characteristic of a circumcenter? Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.22Math Blaster Geometry
UNIT 2 – ANSWER KEYLESSON 14.A.1. scalene, obtuse2. isosceles, equilateral, acute, equiangular3. scalene, rightB. Drawings may vary. Samples are provided.1.Right isosceles triangle135LESSON 21. BAC ABC BCA 180 and BCA 70 , so BAC ABC 110 .12Right scalene triangle2.2. ABE 40 40 100 , so ABE 20 .Students might continue to label the measuresof the angles in the diagram to find themeasure of ABE. See the diagram below.100 B20 40 Obtuse isosceles triangle with obtuse angleand congruent sides labeled as indicated40 3.A10880 100 EDC2223. Since ACD is a right triangle, AC 3 5 ,2so AC 16 and AC 4. Since DB is themedian, AB BC. So AB 2.16Acute scalene triangle Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.120 60 4. AC 10 since ABC is an equilateral triangle.DB 6, since DC DB.AD 8 using the Pythagorean theorem. CAD 40 , since 90 50 CAD 180 .23unit 2-5answ.epMath Blaster Geometry
UNIT 2 – ANSWER KEYLESSON 3Solutions may vary. Sample answers are provided.1. DC BCETheorem: SAS4. ABD DCATheorem: SSSCBDBCDEA2. ABE CDETheorem: HLAABCE3. AEB CEBTheorem: SSSDunit 2-8answ.epsunit 2-11answ.epsDEA Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.BC24Math Blaster Geometry
UNIT 2 – ANSWER KEYLESSON 41–5. See the labeled map below.Main Street22 miles16 milesAirport10milCross esBlvtod. wn8 miles15th Street6 milesHomeLESSON 56. Home to intersection of 15th and Main:45 mi/60 min 8 mi/x; x 11.Students’ measurements and constructions mayvary. Students should make conclusions similar tothe following for questions 3 and 6:Intersection of 15th and Main to airport:40 mi/60 min 22 mi/x; x 33.3. The incenter of a triangle is equidistant fromunit 2-12answ.epsthe sides.This route would take approximately11 33, or 44 minutes.6. The circumcenter of a triangle is equidistantfrom the vertices.Home to intersection of Crosstown and Main:40 mi/60 min 10 mi/x; x 15.Intersection of Crosstown and Mainto airport:40 mi/60 min 16 mi/x; x 24.This route would take approximately15 24, or 39 minutes. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.25Math Blaster Geometry
UNIT 3 –QUADRILATERALS AND OTHERPOLYGONSLesson 1: Tree DiagramLesson 2: Quadrilateral RelationshipsLesson 3: Concave or Convex?Lesson 4: Cut Out the AnglesLesson 5: Angles of Polygons Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.26Math Blaster Geometry
UNIT 3 – QUADRILATERALS AND OTHER POLYGONSgons. Once this concept is established, studentsexplore regular and irregular polygons, trying toconstruct concave and convex figures. In all ofthese exercises, students discover characteristicsof polygons and the relationships among thesetraits and figures.LESSON 1: TREE DIAGRAMHand out copies of the Tree Diagram activitysheet, p. 28. Help students understand the formatof the diagram (from general to specific). Thisactivity can serve a variety of purposes. Asstudents complete the diagram, they show anunderstanding of the characteristics of a quadrilateral. The organization of the diagram makesit easy to study the relationships between quadrilaterals. The completed tree diagram can beused as a visual reference to answer questionsabout the characteristics of all kinds of quadrilaterals. Have students keep the diagram for usewith Lesson 2.LESSON 4: CUT OUT THE ANGLESHand out copies of the Cut Out the Anglesactivi-ty sheet, p. 31. There are a few differentways to study the sum of the measures of anglesin polygons. This technique involves cutting outthe angles of figures and then placing them sideby side on a straight line. The purpose is to lookfor angles that form a straight angle (180 ).Students manipulate the pieces and get a handson understanding of the concept. During this lesson, you may also wish to take advantage of theopportunity to review angles by looking forexamples of acute, obtuse, right, and supplementary angles.LESSON 2: QUADRILATERALRELATIONSHIPSHand out copies of the QuadrilateralRelation- ships activity sheet, p. 29. Havestudents also take out their completed TreeDiagram activity sheet from Lesson 1.Explain that the diagram includes all the information they need to complete the true-or-false exercise. Students might draw examples of the different quadrilaterals on their diagram, includingall of the characteristics listed.LESSON 5: ANGLES OF POLYGONSHand out copies of the Angles of Polygonsactivity sheet, p. 32. After completing Lesson 4,students should understand what it means to findthe sum of the measures of the angles of a polygon. This activity introduces a formula for findingthis sum in polygons with any number of sides.Students find the sums and then solve problemsthat apply the information. The skills they practicehere will be used in proofs and in other problemsolving situations.LESSON 3: CONCAVE OR CONVEX?Hand out copies of the Concave or Convex?activity sheet, p. 30. Remind students that a diagonal of a figure is a line that connects two vertices, but is not a side of the figure. This activityinvolves examining the diagonals of polygons todevelop definitions for concave and convex poly- Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.27Math Blaster Geometry
UNIT 3LESSON 1NAMETREE DIAGRAMUnder each figure name is one or more lines for listing the characteristics of thatfigure. Any figure that falls below another on the tree has its own characteristicsas well as the characteristics of the figures above it. For example, a rhombus hasall of the characteristics of a parallelogram and quadrilateral as well as two additional traits of its own. From top to bottom, the figures in the tree go from generalto more specific.Directions: Choose from the list below. Write the characteristics where they belongin the tree. Each characteristic is used only once. Diagonals bisect each otherHas 4 right anglesHas exactly 1 pair of parallel sidesHas 2 pairs of parallel sidesHas 4 sidesOpposite angles are congruent Has 4 congruent sidesHas 2 pairs of congruent sidesHas exactly 2 congruent legsAll sides are different lengthsDiagonals are perpendicular toeach hombusScaleneRectangleSquare Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.28Math Blaster Geometry
UNIT 3LESSON 2QUADRILATERAL RELATIONSHIPS NAMEDirections: Use your completed tree diagram from Lesson 1 to help determinewhether each statement below is true or false. Write T or F on the lines.1. A rectangle is a quadrilateral.2. A rhombus is a rectangle.3. A square is a parallelogram.4. An isosceles trapezoid is a parallelogram.5. A square is a rectangle.6. A rectangle is a square.7. A rectangle is a parallelogram.8. A parallelogram is a rectangle.9. The diagonals of a square bisect each other.10. The diagonals of a rectangle are perpendicular.11. An isosceles trapezoid has two pairs of congruent sides.12. Opposite angles of a rhombus are congruent.13. A parallelogram has four right angles.14. The diagonals of a square are perpendicular bisectors of each other.15. The diagonals of a parallelogram are perpendicular. Vivendi Universal Publishing and/orits subsidiaries. All Rights Reserved.29Math Blaster Geometry
UNIT 3LESSON 3NAMECONCAVE OR CONVEX?A. Directions: Draw all the diagonals for each figure below. Then answer the questions.ConvexCConcaveConcaveConvexC
always, sometimes, or never. 1. A line is _ labeled by a single lowercase letter. 2. If two distinct lines intersect, they _ intersect at exactly one point. 3. If two planes intersect, they _ intersect at exactly one point. 4. Two collinear points are _ coplanar. 5.
Mounting the Air Blaster to the discharge pipe 13 General piping instructions for Air Blaster System air control components 14 Air Blaster control components installation 15 IV. AIR BLASTER START-UP PROCEDURES 19 V. MAINTENANCE 19 VI. DISASSEMBLY AND ASSEMBLY OF THE AIR BLASTER 20 Dismounting the Air Blaster 20 Removing the internal valve 21 .
children who join GC and Blaster in a fun and lively reading adventure. Join GC, Blaster, and their pal Mel as they jet off to the Aquatic Moon in search of lost treasures. Reading Blaster Ages 4–6 is an exciting new addition to the Blaster family of products. A variety of phonics skills, word
Charging The Battery Pack For The First Time Only charge the Pool Blaster with the charger provided with the unit. The charger provided is specially designed for the Pool Blaster. Please note that the Battery Pack for your Pool Blaster has been shipped in a low voltage condition. You must charge the Pool Blaster Battery Pack
the MICRO-BLASTER so that the Firing Pin extends about 1/10 of an inch from the tip of the MICRO-BLASTER. A whipping motion seems the most effective for extending the Firing Pin. If the Firing Pin is not easily shifted, check for damage or dirt which may be stopping its free movement. NEVER USE YOUR MICRO-BLASTER IF THE FIRING PIN DOES NOT MOVE
Reading Blaster Vocabulary is an entertaining, content-rich CD-ROM program that encourages students to use a range of language arts skills to boost their vocabulary. Reading Blaster Vocabulary contains over 2,000 age-appropriate words. As students explore room after room of Biza
Adventure tourism is a rapidly expanding sector of the tourism industry internationally. New Zealand is internationally recognised as a country where adventure tourism and adventure sports are undertaken by a large proportion of the resident and visitor population. While the risks associated with adventure tourism and adventure sport activity are increasingly highlighted in media reports of .
KTM 990 Supermoto / R / Adventure 2009 / 16 S-R1 1290 Adventure / S 2015 / 20 R1 1190 Adventure / R 2013 / 16 R1 1090 Adventure / R 2018 / 19 R-1 1050 Adventure 2016 / 17 R1 790 Adventure / R 2019 / 20 S-R1 890 Duke R 2020 S-R1 990 Superduke / R 2009 / 16 S-R1 1290 Superduke 2014 / 16 S-R1 1290 Superduke 2017 / 18 S-R1 1290 Superduke 2019 / 20 S-R1
adventure, “Escape the Tomb.” If you’re playing your first game with friends, play the second adventure, “Find the the dungeon and begin their adventure. It’s twice the size of the Icon of Ravenloft.” Check the “Adventure Setup” section of the Adventure Book to see if your chosen Adventure calls for any of the
