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NameDateLINES AND ANGLESLines, line segments, and rays are straight paths.LineA line is a straight paththat goes on without end intwo directions.ALine SegmentRayA line segment is a part of A ray is a part of a line. Ita line. It has two endpoints. has one endpoint and goeson without end in onedirection.CBIntersecting LinesIntersecting lines are linesthat cross at one point.EGB Discovery Education. All Rights Reserved.FMNQRline MN is parallel to lineQRName each figure.H2.BCAP[ray PQ]Parallel LinesParallel lines are lines in oneplane that never intersect.Hline EF isperpendicularto line GHline AB and line CDintersect at point EQKray JKPerpendicular LinesPerpendicularlines intersectat right angles. ECD1.Jline segment CDline ABADD[perpendicular lines3.GKJ[parallel lines GH and JK]4.XY[line XY]AB and CD]CHALLENGEDraw and label a diagram to illustrate each of the following: [Check students’ drawings.]line GH parallel to line LMline RS and line XZ intersecting at point PLEVELDiscovering Math, Geometry, Lines and Angles.or, Coming Together2

NameDateLINES AND ANGLESLineA line is a straight paththat goes on without end intwo directions.ABRayLine SegmentA line segment is a part of A ray is a part of a line. Ita line. It has two endpoints. has one endpoint and goeson without end in oneCDdirection.line AB or AB orline BA or BA orline segment CD or CDline segment DC or D C Intersecting LinesIntersecting lines are linesthat cross at one point.Perpendicular LinesPerpendicular lines intersectat right angles.AEDG AB and CD intersect atpoint EK ray JK or JKECBJParallel LinesParallel lines are lines inone plane that neverintersect.H GHEF F means“is perpendicular to”MNQR MN QR means “is parallel to” Discovery Education. All Rights Reserved.Use the figure at the right to name an example of each term.[Sample answers given]1. perpendicular lines2. ray3. line segment4. intersecting lines5. parallel lines6. lineDraw and label a figure for each. [Check student’s drawings.]7. line FGST8. PQ 9. RS M NLEVELDiscovering Math, Geometry, Lines and Angles.or, Coming Together3

NameDateMAP AND DRAWING SCALESA map is a diagram that showsrelationships among places, often includingdistance information.This map shows some places3 milesnear Bev’s house.The map shows that Bev lives 4 milesfrom her school.6 miles1 mile2 miles1 mile4 miles5 milesUse the map above to answer each question.1. How many miles is Bev’s house from the library?2. How many miles does Karl live from the mall?[6 miles][2 miles]3. Who lives closer to school, Bev or Karl? How much closer?[Bev lives 1 mile closer.]4. Bev goes from her house, to the library, and then to the post office. Atthat point, how far did she travel?[9 miles]5. How many miles is a round trip from Karl’s house to school and back? Discovery Education. All Rights Reserved.[10 miles]6. Who lives closer to the library, Bev or Karl? Explain.[Karl lives closer. He can travel either 3 miles or 4 miles to the library.Bev lives 6 miles from the library.]CHALLENGEWhat is the shortest route to the school from the library shown on the map?What is the distance?[Start at the library. Go 1 mile to the mall, 2 miles to Karl’s house,then 5 miles to the school. The distance is 8 miles.]LEVELDiscovering Math, Geometry, Maps and Drawing Scales.or, Scaling Peaks1

NameDateMAP AND DRAWING SCALESA map is a diagram that shows distances between different locations.The map below shows some trails in a forest.It is 1 mile between each pair of circle markers shown on the map.So, it is 6 miles from the trailhead to the top of the Trail A.TrailheadUse the map above to answer each question.1. How far is it from the trailhead to the top of Trail B?[5 miles]2. How far is it from the trailhead to the top of Trail C?[7 miles]3. Trail D connects Trails B and C. How long is Trail D?[3 miles] Discovery Education. All Rights Reserved.4. Start at the trailhead and start to follow Trail B. Then go along Trail D tothe top of Trail C. How far is it to the top?[7 miles]5. What is the total roundtrip distance from the trailhead to the top of TrailA and back?[12 miles]6. What is the shortest total distance of a hike that starts at Trail C,turns onto Trail D and then follows Trail B to the trailhead of Trail B?[10 miles]7. How much longer is a roundtrip hike from the trailhead to the top ofTrail C than a roundtrip hike to the top of Trail A?[2 miles]CHALLENGESuppose the distance between each pair of markers on the map were 5miles. How far would it be to the top of Trail A? Explain.[30 miles; Possible explanations: 6 5 30 or count by 5s between markers.]LEVELDiscovering Math, Geometry, Maps and Drawing Scales.or, Scaling Peaks2

NameDateMAP AND DRAWING SCALESA scale drawing is a drawingthat showsa real object enlarged or reduced.The scale is a ratio that compares the sizeof the object in the drawing to the sizeof the actual object.The map shows the locationof 7 differentsites an archaeologist is mapping.Scale1 in. 12 miWhat is the actual distance between Site A and Site B?The map uses the scale 1 inch 12 miles.Use a ruler to measure the distance from Site A to Site B on the map.The distance on the map is 2 12 or 2.5 inchesFind an equivalent ratio to find the actual distance.actual distanceactual distance12 mi? 1 in.2.5map scale distancemap scale distance Discovery Education. All Rights Reserved.Think: 2.5 12 3012 mi 1 in.30 mi 2.5 miThe actual distance between the sites is 30 miles.Use the above map and map scale to find each distance.1. What is the actual distance between Site B and Site C?[36 mi]2. What is the actual distance between Site C and Site D?[24 mi]3. What is the actual distance between Site D and Site E?[18 mi]4. What is the actual distance between Site E and Site F?[12 mi]5. What is the actual distance between Site F and Site G?[6 mi]LEVELDiscovering Math, Geometry, Maps and Drawing Scales.or, Scaling Peaks3

NameDateSHAPE NAMESThree-Dimensional Figures or Space FiguresRectangular PrismCylinderConeSphereTwo-Dimensional Figures or Plane FiguresSquareRectangleTriangleCircleName each shape.1.[triangle]5. Discovery Education. All Rights Reserved.3.2.[rectangular der][rectangle]9. Which figures in the exercises are plane figures?[1, 3, 6, 8]10. Which figures in the exercises are space figures?[2, 4, 5, 7]CHALLENGEName a real-life example of a rectangular prism, a cylinder, a cone, anda sphere.[Answers may vary. Possible answers: rectangular prism: cereal box;cylinder: can of soup; cone: ice cream cone; sphere: ball]Discovering Math, Geometry, Shape Names.or, Get in ShapeLEVEL1

NameDateSHAPE NAMESThree-Dimensional agonoctagonName each figure. Discovery Education. All Rights Reserved.1.2.[square sphere][triangle]8.[hexagon][cone]CHALLENGEA polygon with four sides is called a quadrilateral. Draw a quadrilateral thatis not a rectangle. Then draw another quadrilateral that is not aparallelogram and not a trapezoid. [Check students’ drawings.]LEVELDiscovering Math, Geometry, Shape Names.or, Get in Shape2

NameDateSHAPE ctagon3 sides3 angles4 sides4 angles5 sides5 angles6 sides6 angles8 sides8 anglesSpecial usSquareOnly twoparallel sides.Opposite sidesare parallel andthe same length.Parallelogramwith 4 rightangles.Parallelogramwith all sides thesame length.Rectangle withall sides thesame length. Discovery Education. All Rights Reserved.Name each gon]Classify each quadrilateral. Some may have more than one llelogram, rectangle,rhombus, square]LEVELDiscovering Math, Geometry, Shape Names.or, Get in Shape3

NameDatePROPERTIES OF GEOMETRIC FIGURESAnglesRight AngleA right angle forms asquare corner.Acute AngleAn acute angle is less thana right angle.Obtuse AngleAn obtuse angle is greaterthan a right angle.The square in the cornermeans the angle is a rightangle.Tell whether each angle is right, acute, or obtuse.1.2.[acute]3.[right]4.[obtuse][acute] Discovery Education. All Rights Reserved.Tell whether the angle each arrow points to is right, acute, or LLENGEDraw a triangle with an obtuse angle. [Check students’ drawings.]LEVELDiscovering Math, Geometry, Properties of Geometric Figures.or, Information in Forms1

NameDatePROPERTIES OF GEOMETRIC FIGURESAnglesRight AngleA right angle forms asquare corner.Acute AngleAn acute angle is less thana right angle.Obtuse AngleAn obtuse angle is greaterthan a right angle.An angle can be named in three ways. B or ABC or CBARead: angle B or angle ABC or angle CBATwo rays meet at an endpoint to form an angle.The endpoint is always included in the angle name.Tell whether each angle is right, acute, or obtuse. Discovery Education. All Rights Reserved.1.2.[acute]3.[right]4.[obtuse][acute]For each figure, tell whether ABC is right, acute, or ENGEClassify each of the anglesof the parallelogram.[angles A and C are acute and angles B and D are obtuse]Discovering Math, Geometry, Properties of Geometric Figures.or, Information in FormsLEVEL2

NameDatePROPERTIES OF GEOMETRIC FIGURESAn angle is formed when two rays meet at the same endpoint, or vertex.The angle can be named by three letters or by its vertex:ray B or ABC or CBAvertexrayAngles are measured in degrees ( ).Right AngleA right anglemeasures 90 .Acute AngleAn acute angle isgreater than 0 and less than 90 .Use the figure below. Tell whethereach angle is right, acute,obtuse, or straight.Obtuse AngleAn obtuse angle isgreater than 90 and less than 180 .1. DCG2. GDE[right]3. CDE Discovery Education. All Rights Reserved.Straight AngleA straight anglemeasures 180 .[straight]4. CDG[obtuse]Use the figure below. Name as many 5. acuteexamples of each type of angle[ QJK or KLS]as possible.7. right[acute]6. obtuse[ JKR or RKL]8. straight[ JQR or QRK or[ QRS] KRS or RSL]LEVELDiscovering Math, Geometry, Properties of Geometric Figures.or, Information in Forms3

NameDateALTERING SHAPESShapes can be combined to make differentshapes.Joining two squares makes a rectangle:Shapes can be divided to make differentshapes.Dividing a rectangle along the diagonalmakes two triangles:Name the shapes used to make each figure.1.2.[square and 2 triangles]3.[rectangle and 2 triangles]4. Discovery Education. All Rights Reserved.[square and triangle]5.[2 rectangles and 4 triangles]6.[6 triangles][3 rectangles]CHALLENGEMake a new shape by combining at least 3 different geometric shapes.[Check students’ drawings.]LEVELDiscovering Math, Geometry, Altering Shapes.or, Shape Shifting1

NameDateALTERING SHAPESPolygons can be combined to makedifferent polygons.Polygons can be divided to make differentpolygons.Joining a square and two triangles makesa trapezoid:Dividing a parallelogram along thediagonal makes two triangles:Name the polygons used to make each figure.Then identify the figure.1.2.[rectangle and 2 triangles; hexagon] Discovery Education. All Rights Reserved.3.[triangle and trapezoid; parallelogram]4.[4 triangles; pentagon]5.[2 parallelograms; hexagon]6.[2 trapezoids; hexagon][trapezoid, 2 rectangles, 2 triangles; octagon]CHALLENGEMake a new shape by combining at least 3 different polygons.[Check students’ drawings.]LEVELDiscovering Math, Geometry, Altering Shapes.or, Shape Shifting2

NameDateALTERING SHAPESPolygons can be combined to makedifferent polygons.Polygons can be divided to make differentpolygons.Joining two parallelograms can make ahexagon:A hexagon can be divided into twotrapezoids:Name the polygons used to make each figure. Then identify the figure.1.2.[5 triangles; pentagon]3.[trapezoid and 2 triangles; trapezoid]4.[2 trapezoids and rectangle; octagon] Discovery Education. All Rights Reserved.5.[triangle and trapezoid; pentagon]6.[4 triangles; rhombus][4 triangles; parallelogram]CHALLENGE [Check students’ drawings. Sample answers shown.]Make a pentagonby joining together4 triangles.Make a hexagonby joining together6 triangles.LEVELDiscovering Math, Geometry, Altering Shapes.or, Shape Shifting3

NameDateCONGRUENT AND SIMILAR SHAPESCongruent FiguresThese rectangles are congruent.Congruent figures have the same shapeand the same size.Similar FiguresThese rectangles are similar.Similar figures have the same shape butnot the same size.Are the figures congruent, similar, or neither?1.2.[similar]3.[congruent]4. Discovery Education. All Rights er]8.[congruent][neither]LEVELDiscovering Math, Geometry, Congruent and Similar Shapes.or, Same Difference1

NameDateCONGRUENT AND SIMILAR SHAPESCongruent FiguresCongruent figures havethe same shape andthe same size.Similar FiguresSimilar figures havethe same shape butnot the same size.The rectangles are similar.The rectangles are congruent.Are the figures congruent, similar, or neither?1.2.[congruent] Discovery Education. All Rights gruent][neither]CHALLENGEDanny takes a photograph of his house. Then he has the photographenlarged. Is the house in the enlargement congruent to the house in theoriginal photograph? Is it similar? Explain.[It is not congruent because the enlargement is larger than the original.It is similar since everything should be enlarged by the same ratio.]Discovering Math, Geometry, Congruent and Similar Shapes.or, Same DifferenceLEVEL2

NameDateCONGRUENT AND SIMILAR SHAPESSimilar FiguresCongruent FiguresSimilar figures havethe same shape butnot the same size.Congruent figures havethe same shapeand the same size.The triangles are similar.The corresponding angles of the trianglesare equal. The ratios of correspondingsides are equal.The triangles are congruent.Since they are the same shape,the triangles are also similar. The ratios ofcorresponding sides of the triangles is 1:1.Are the figures congruent, similar, neither, or both?2.1.[similar] Discovery Education. All Rights Reserved.3.[neither]4.[both][neither]CHALLENGEDraw a rectangle on the grid.Then draw a rectangle that is similarbut not congruent to your rectangle.[Check students’ drawings.]Explain how you know the rectanglesare similar.[Answers may vary. Possible answer: I doubled both the lengthand the width of my original rectangle to draw the similar rectangle.]LEVELDiscovering Math, Geometry, Congruent and Similar Shapes.or, Same Difference3

NameDateMOTION GEOMETRYTranslationA translation slides afigure along a straightline left, right, up,or down.ReflectionA reflection flips a figure across a line.A reflection makes a mirror image.RotationA rotation turns a figure around a point.Write translation, reflection, or rotation to describe how each figurewas moved.1.2. Discovery Education. All Rights ][rotation]CHALLENGEIs the reflection of a figure congruent to the original figure? Explain.[Yes. The figure is still the same size and shape. Only its position has changed.]LEVELDiscovering Math, Geometry, Motion Geometry.or, Drag ‘n’ Flip1

NameDateMOTION GEOMETRYTranslationA translation slides a figurealong a straight line left,right, up, or down.ReflectionA reflection flips a figureacross a line. A reflectionmakes a mirror image.RotationA rotation is a turn thatmoves a figure around apoint.Write translation, reflection, or rotation to describe how each figurewas moved.1.2.[translation] Discovery Education. All Rights 6.[rotation][reflection]CHALLENGETranslations, reflections, and rotations are transformations of a figure.Do these transformations result in a figure congruent to the original figure?Explain.[Yes. For these transformations, the transformed figure is still the same size and shape.Only its position has changed.]LEVELDiscovering Math, Geometry, Motion Geometry.or, Drag ‘n’ Flip2

NameDateMOTION GEOMETRYA transformation moves a figure without changing its size or shape.TransformationsTranslationReflectionA translation moves a figure A reflection flips a figurealong a straight line.across a line. A reflectionmakes a mirror image.RotationA rotation moves a figureby turning it around apoint. All the points on thefigure move in a circle.Some points move fartherthan others, dependingon how far fromthe center ofrotation they are.Write translation, reflection, or rotation to describe how each figure wasmoved. Discovery Education. All Rights n][reflection]CHALLENGEDraw a translation, reflection, androtation of the triangle shown onthe grid. Label each transformation.[Check students’ drawings.]LEVELDiscovering Math, Geometry, Motion Geometry.or, Drag ‘n’ Flip3

NameDateLINES AND ANGLESLines, line segments, and rays are straight paths.LineA line goes on without endin two directions.Line SegmentA line segment has twoendpoints.RayA ray has one endpointand goes on without end inone direction.Special Types of LinesIntersectingIntersecting lines are linesthat cross at one point.PerpendicularPerpendicular lines cross atright angles.ParallelParallel lines are lines inone plane that never cross. Discovery Education. All Rights Reserved.Name each figure.1.2.[ray]4.3.[perpendicular lines][parallel lines][line segment]CHALLENGEWhich statement is always true? Explain.(a) Intersecting lines are always perpendicular.(b) Perpendicular lines always intersect.[(b) is always true because perpendicular lines intersect at right angles. Intersectinglines do not always cross at right angles.]Discovering M

Discovering Math, Geometry, Properties of Geometric Figures.or, Information in Forms Name Date L E V E L 3 An angle is formed when two rays meet at the same endpoint, or vertex. The angle can be named by three letters or by its vertex: Angles are measured in degrees ( ). Use the figure b