Geometry‐Unit 1: Tools Of Geometry

Geometry‐Unit 1:MonTueTools of GeometryWedThuFriAug 26Aug 27Aug 28Aug 29Aug 30Introductions,Expectations,Course Outline andCarnegieReview summer packetTopic: (1-1)Points, Lines, & PlanesTopic: (1-2)Segment MeasureQuiz on summer packetHWHWSept 2Sept 3Sept 4Sept 5 (Two-Hour Delay)Sept 6Topic: (1-3)Segment MeasureTopic: (1-2 & 1-3)Segment MeasureQuiz 1-1 through 1-3Topic: (1-4)Angle MeasureCarnegie DayHWHWSept 9Sept 10Sept 11Sept 12Sept 13Topic: (1-4)Angle MeasureTopic: (1-5)Angle PairsTopic: (1-5)Angle PairsQuiz 1-4 & 1-5Carnegie DayHWHWHWSept 16Sept 17Sept 18Sept 19Sept 20Study GuideUnit 1 TestHWCarnegie DayThis is a tentative schedule, date may change. Please be sure to write down homework assignments daily.1

Geometry‐Unit 1:Tools of GeometryTopic: Unit 1(12 days) - Tools of Geometry (Chapter 1)Key Learning(s): Students will learn the basic geometryterms and there use for continuing geometry.Optional Instructional ToolsRuler, protractor, graph/number linepaperUnit Essential Question(s): Why is it important to learn thebasic geometry terms and concepts before continuing thecourse?Concept:Points, Lines & Planes(1.1 – 1 days)Lesson EQ’s:What are the basic terms andtheir importance toGeometry?Vocabulary:Point, line, plane, collinear,coplanar, spaceStandards:Concept:Segment Measure(1.2, 1.3 – 3 days)Lesson EQ’s:How are the lengths ofsegments used in everyday life?Concept:Angle Measure(1.4 – 2 days)Lesson EQ’s:Why do we need to understandand use angles in Geometry?Concept:Angle Pairs(1.5 – 2 days)Lesson EQ’s:How are the pairs of anglesclassified?Vocabulary:Line segment, segment additionpostulate, between, congruent,precision, constructions,midpoint, segment bisector,distanceStandards:M11.C.3.1.1 Calculate thedistance and/or midpointbetween 2 points on a numberline or on a coordinate planeG.2.1.2.1 Calculate the distanceand/or midpoint between twopoints on a number line or on acoordinate planeVocabulary:Degree, vertex, ray, opposite ray,angles, sides, interior, exterior,acute angle, obtuse angle, rightangleVocabulary:Vertical angles, linear angles,adjacent angles, complementaryangles, supplementary anglesStandards:M11.B.2.1.1 Measure and/orcompare angles in degrees (up to360 ) (protractor must beprovided or drawn).Standards:M11.B.2.1.1 Measure and/orcompare angles in degrees (up to360 ) (protractor must beprovided or drawn).2

Geometry‐Unit 1:PointLineTools of gmentRayAngle

Geometry‐Unit 1:Tools of GeometryDefine the following:Space-Collinear-Coplanar-Naming Lines and Planes (See Chart)PictureFigure to nameA point on theplane.How did you label it?EHDFA line thatcontains pointGNA planeGA point not onthe plane.4

Geometry‐Unit 1:Tools of GeometryDrawing a Geometric Figure1. Together:a. TU lies in the plane Q and contains the point R.2. Check Your Progress (On Your Own)a. Draw and label a figure in which points A, B, and C are coplanar and B and C are collinear.GInterpret Drawings:1.FDTogether, we will answer questions based on the picture to right:a. How many planes appear in this figure?ABb. Name three collinear points.Ec. Are points G, A, B, and D coplanar?d. Where doesEF and AB intersect?e. Name the intersection of plane GCD and plane P.Reflection: What types of everyday objects could we use to represent these types of undefined terms?PointsLinesPlanes5CP

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Geometry‐Unit 1:Tools of GeometryDefine the following vocabulary words: Be sure to use complete sentences Include an example or picture Relate it to real ance7Real Life Connection

Geometry‐Unit 1:Tools of GeometryDefinition:Example 2: Find x and KL5x – 102xJx 2KLExample 1: Find the value of x and KL27J3xK6xL1.2SegmentAdditionExample 3: Find the value ofExample 4: Find x and LMPostulate30x and ST if S is between R and Tand: RS 7, ST 3x, and RT 25N86x ‐ 5L2x 3M

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Geometry‐Unit 1:Given the coordinate plane(Two ordered pairs)Tools of GeometryFind theDistanceStep 1: Write formula fromFormula SheetGiven a number lineCount the spaces betweenthe two given points.Step 2: Substitute x and yfrom the two given pointsStep 3: EvaluateGUIDED PRACTICEExample: Find the distance between (2, 3)and (6,6)Example: Find the distance betweenA and Bd ( x2 x1 ) 2 ( y 2 y1 ) 2AExample: Find the distance between (1, 4)and (6,8)CBExample: Find the distance betweenD and Fd ( x2 x1 ) 2 ( y 2 y1 ) 2D10FE

Geometry‐Unit 1:Given the coordinate planeTools of GeometryFind theMidpointGiven a number line(Two ordered pairs)Step 1: Write formula fromFormula SheetCount the spaces betweenthe two given points.Step 2: Substitute x and yfrom the two given pointsDivide by 2Step 3: EvaluateGUIDED PRACTICEExample: Find the midpoint between (2, 3)and (6,6)Example: Find the midpoint betweenA and B x2 x1 y 2 y1 , 2 2AExample: Find the midpoint between (1, 4)and (6,8)CBExample: Find the midpoint betweenD and F x2 x1 y 2 y1 , 2 2D11FE

Geometry‐Unit 1:ABCDEFTools of GeometryGHJKLMFind the length of each segment using the number line above:1.AD2.HL3.EJ4.CG7.DF8.BG34Find the midpoint of the given segments using the number line above5.AC-116.-8-5JM-3 -205811Find the length of each segment given the two endpoints from the number line above9. -8 and 510. -3 and 11Distance formula:11. -11 and -2Midpoint formula:Find the distance between the two points1. (5, 1) (-3, -3)2. (3, -4) (-2, -10)3. (-5, 6) (8, -4)5. (5, 12) (-4, 8)6. Given J(-5, 10) and the midpoint ofFind the midpoint between the two points4. (5, -2) (-1, 6)JK is (-8, 6) find the coordinate for K12

Geometry‐Unit 1:Tools of GeometryHomework 1‐313

Geometry‐Unit 1:Tools of GeometryDefine the following vocabulary words: Be sure to use complete sentences Include an example or picture Relate it to real lifeWordVertexDefinitionPicture/ExampleRays (Sides)StraightAngleAngleRight AngleAcute AngleObtuse Angle14Real Life Connection

Geometry‐Unit 1:Tools of GeometryACBAngles and Their PartsX1.WTogether, we are going to identify parts using the diagram to the righta. Name 3 angles that have W as a vertex.13V2ZYb. Name all the sides of 1 .c. Write another name for WYZ .d. Name a pair of opposite rays.EBACDHow to read a protractor:1. Put the dot in the center on the vertex2. Line up the protractor with one of the rays crossing the 03. Read where the arrow crosses and use the correct number. (Big Angle Big #, Small Angle Small #)Find:m ADC m BDC 15m BDA (challenge problem)

Geometry‐Unit 1:Tools of GeometryHow to draw angles using a protractor:1. Draw a ray2. Place protractor with center dot at endpoint on ray3. Using the numbers carefully mark the number you need on the outside of the protractor4. Draw a new ray from the endpoint to the mark you made80o95o120o100o16

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Geometry‐Unit 1:Tools of GeometryOpposite Rays The rays that form an angle are called the .The common endpoint is the .The is the points inside the angle.The is the points outside the angle.Angles can be classified by their measuresStraightRightAcuteClassify each angle:1.2.3.4.5.6.18Obtuse

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Geometry‐Unit 1:Tools of GeometryDefine the following vocabulary words: Be sure to use complete sentences Include an example or picture Relate it to real lifeWordDefinitionPicture/ExampleVertical AnglesLinear AnglesAdjacent AnglesComplementaryAnglesSupplementaryAngles20Real Life Connection

Geometry‐Unit 1:Tools of GeometryUsing Algebra with Angles1. Together we will solve for:AC(6x 2)oa. Suppose ABC DBF as shown,find the actual measure of each angle.BD(8x‐14)oEb. Suppose QP and QR are opposite rays, and QT bisects RQS . If RQT 6x 5 and SQT 7x ‐2. Find the measure of RQT .2. Check Your Progress (On Your Own)i. Hint Draw a Diagram to help you visualize.a. Suppose JKL MKN . If JKL 5x 4 and MKN 3x 12. Find the actual measure ofeach angle.b. Suppose QP and QR are opposite rays, and RQT 12a‐8. Find the measure of TQS .21QTbisects RQS . If RQS 22a ‐11 and

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Geometry‐Unit 1:Tools of GeometryAngle Practice: Look at the picture, then determine what type of angles you have and how to find their measure usingthe boxes provided. Then SOLVE for x, and find the measurement of each angle!Circle the type of angle you have and the measurement:Vertical3x 202x 56ComplementarySupplementaryAre they equal to?Each otherNinety DegreesOne‐hundred EightySolution:Circle the type of angle you have and the measurement:Vertical4x 402x 20ComplementarySupplementaryAre they equal to?Each otherNinety DegreesOne‐hundred EightySolution:Circle the type of angle you have and the e they equal to?4xEach otherSolution:25Ninety DegreesOne‐hundred Eighty

Geometry‐Unit 1:Tools of GeometryCircle the type of angle you have and the measurement:Vertical3x 205x ‐ 56ComplementarySupplementaryAre they equal to?Each otherNinety DegreesOne‐hundred EightySolution:Circle the type of angle you have and the measurement:Verticalx 402x 20ComplementarySupplementaryAre they equal to?Each otherNinety DegreesOne‐hundred EightySolution:Circle the type of angle you have and the e they equal to?7xEach otherSolution:26Ninety DegreesOne‐hundred Eighty

Geometry‐Unit 1:Tools of GeometryAngle Homework: Look at the picture, then determine what type of angles you have and how to find their measureusing the boxes provided. Then SOLVE for x, and find the measurement of each angle!Circle the type of angle you have and the measurement:2x 25VerticalComplementarySupplementaryAre they equal to?4x ‐ 15Each otherNinety DegreesOne‐hundred EightySolution:Circle the type of angle you have and the measurement:Vertical3x 352xComplementarySupplementaryAre they equal to?Each otherNinety DegreesOne‐hundred EightySolution:Circle the type of angle you have and the Are they equal to?Each otherSolution:27Ninety DegreesOne‐hundred Eighty

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Geometry‐Unit 1: Tools of Geometry 5 Drawing a Geometric Figure 1. Together: a. TU lies in the plane Q and contains the point R. 2. Check Your Progress (On Your Own) a. Draw and label a figure in which points A, B, and C are coplanar and B and C are collinear.