Lines, angles and shapes – parallel and perpendicular linesParallel lines are always the same distanceaway from each other at any point andcan never meet. They can be any lengthand go in any direcƟon.1Look at each group of lines. Trace over any parallel lines with a coloured pencil:abcPerpendicular lines meet at right angles.SomeƟmes they intersect (cross over),someƟmes they do not intersect.2Trace each pair of perpendicular lines with a coloured pencil:a3bcIn this space, draw three pairs of parallel lines and three pairs of perpendicular lines:Answers will vary.Space, Shape, and PositionCopyright 3P LearningE1SERIESTOPIC1
Lines, angles and shapes – anglesAn angle is the amount of turning between two lines that meet.There are three classificaƟons of angles depending on their size.A right angle is 90 (degrees).1An acute angle is smallerthan a right angle.Classify each angle as right, acute or obtuse.abobtusedcacuteeobtuse2rightfrightacuteDraw hands on each clock that show a Ɵme for each type of angle.aRight anglebObtuse anglePossible answers.2An obtuse angle is largerthan a right angle.E1SERIESTOPICSpace, Shape, and PositionCopyright 3P LearningcAcute angle
Lines, angles and shapes – angles3Use your ruler to draw three more examples of each type of angle.a Right anglesAnswers will vary.b Acute anglesc Obtuse angles4Complete each closed shape according to the direcƟons:Shape a has 2 acute angles.Shape b has 5 right angles.Shape c has 2 acute and 2 obtuse angles.abcSpace, Shape, and PositionCopyright 3P LearningE1SERIESTOPIC3
Lines, angles and shapes – polygons and quadrilaterals 1Polygons are shapes with 3 or more sides.Quadrilaterals are shapes with 4 sides.1Check the polygons. Circle the quadrilaterals. 2 Complete this table:Name3 Number of sidesNumber of hexagon66fsquare44grectangle44htriangle33Name one shape that is both a quadrilateral and a polygon:square/rectangle /rhombus4Why is a circle not a polygon?Apolygon must have straight sides.4E1SERIESTOPICSpace, Shape, and PositionCopyright 3P Learning
Lines, angles and shapes – types of quadrilateralsA parallelogram is a quadrilateral with 2 pairs of parallel sides.This is a parallelogram. Its opposite sides arean equal length and are parallel to each other.A square and a rectangle are also parallelograms.They have opposite sides that are equal lengthsand are parallel to each other.A rhombus is a parallelogram. Its opposite sidesare an equal length and are parallel to each other.It has 4 equal sides.1How many pairs of parallel lines are there in these parallelograms?Count them:2Write the number of shapes you can see in the box above.Name22Number of ams11equadrilaterals11Space, Shape, and PositionCopyright 3P LearningE1SERIESTOPIC5
Lines, angles and shapes – types of quadrilateralsA trapezoid is a quadrilateral and has one pair of parallel sides.3Check your understanding of types of parallelograms and trapezoids.a Draw a shape with two pairs of parallelsides and sides that are equal in length. squareThis shape is a .c Draw a shape with two pairs of parallelsides and opposite sides that are equal.trapezoidThis shape is a .d Draw another parallelogram that isdiﬀerent to the others. parallelogramThis shape is a .6b Draw a shape with one pair ofparallel sides.E1SERIESTOPICrectangleThis shape is a .Space, Shape, and PositionCopyright 3P Learning
Lines, angles and shapes – polygons and quadrilaterals 212Decide whethereach shape inthe table is aquadrilateral ora polygon or both.Write yes or anglenoyesDraw lines to connect the shapes to the labels. Then put a check in the shapes whichare quadrilaterals and circle the parallelograms. The first one has been done for you. rhombusSome labels mighthave more than oneconnecƟng line.squarerectangle pentagon4 sideshexagon5 sidestrapezoid6 sidesoctagon8 sides Space, Shape, and PositionCopyright 3P LearningE1SERIESTOPIC7
Lines, angles and shapes – symmetryA shape is symmetrical when you can fold it in half sothat one half exactly covers the other half. The fold lineis the axis of symmetry. Many 2D shapes have morethan one line of symmetry.This shape has 4 linesof symmetry.1 Copythis pageand cutout eachshape.Find all the linesof symmetry.See how manydiﬀerent waysyou can foldeach shape inhalf. Then drawin all the linesof symmetry onthe shapes onthis page.copyabcdTeacher check.28Use the line of symmetry and a ruler to complete each shape. E1SERIESTOPICSpace, Shape, and PositionCopyright 3P Learning
Symmetrical challengescreateGeƫngreadyFor these challenges, you will need a ruler and a pencil.Whatto doHere are four unfinished symmetrical designs on dot paper.You must must complete them. For each design, you must usea horizontal line, a verƟcal line and two diagonal lines.When they are finished, they will each be symmetrical.For each design, decide where the line of symmetry will be.Pretend the line is a mirror – what will the reflecƟon look like?Teacher check.Space, Shape, and PositionCopyright 3P LearningE1SERIESTOPIC9
Investigating 3D figures – properties of shapesIn this topic, we are looking at the properƟes of 3D figures. The pointy cornerof a 3D figure is called a vertex. The plural is verƟces.Prisms have 2 bases that are the same size and shape and are a type of polygon.Pyramids have only one base. All the faces are triangular and they meet ata common point also known as the apex.1Complete the properƟes of these prisms:aName10hexagonal prismFaces678VerƟces81012121518Complete the properƟes of these pyramids:a3crectangular prism pentagonal prismEdges2bbcNamesquare pyramidFaces567VerƟces567Edges81012pentagonal pyramid hexagonal pyramidMahlia made a 3D figure usingtoothpicks and plasƟcine.She used nine toothpicks andsix pieces of plasƟcine. Circlethe shape she made.E2SERIESTOPICSpace, Shape, and PositionCopyright 3P Learning
Investigating 3D figures – drawing 3D figuresWe can draw 3D figures easily by using dot paper.Example 1For a frontview, usesquare dotpaper.1Step 1Step 2Step 3Draw these shapes on the dot paper below. You might like to try a few Ɵmes.Teacher check.Space, Shape, and PositionCopyright 3P LearningE2SERIESTOPIC11
Investigating 3D figures – drawing 3D figuresExample 2For a cornerview, usetriangulardot paper.2Step 1Step 2Draw these shapes below:aTeacher check.bc12E2SERIESTOPICSpace, Shape, and PositionCopyright 3P LearningStep 3
Investigating 3D figures – different viewpoints1Here are some 3D models made from cubes. Shade in the squares on each grid toshow the top, front and side view for each one. The top view of the first modelhas been done for you.Top ViewviewFront viewSide viewTop viewFront viewSide viewTop viewFront viewSide viewTop viewFront viewSide viewabcdSpace, Shape, and PositionCopyright 3P LearningE2SERIESTOPIC13
Investigating 3D figures – cross sectionsA cross secƟon is what you see when you slice rightthrough something.12Draw the cross secƟon next to each shape:abcdefDraw a line on each shape to show where you would cut to get the smallestpossible circle.a14bE2SERIESTOPICSpace, Shape, and PositionCopyright 3P Learning
Investigating 3D figures – netsA net is the flat shape that a 3D figure can be constructed from.copy1Draw a line to match these 3D figures with the nets below:2Which of these nets will fold into a cube? You may like to ask your teacher to copythis page and enlarge the nets below so you can invesƟgate. Check the nets thatwork and cross the nets that don’t. Space, Shape, and PositionCopyright 3P Learning E2SERIESTOPIC15
Dice puzzlesolveGeƫngreadyIn these two dice puzzles, you have to use the clues to imaginewhich face has which number.Whatto doDice Puzzle 1Write the numbers 1 to 6on this net of the cube if:1a 2 is opposite 6.b 3 is opposite 5.13 2 5 64c 1 is opposite 4.Sample3answers.245623 1 5 46Dice Puzzle 2Chelsea made a die from a cardboard net of a cube. She putss cker dots to represent the numbers on each side of the cube.Here is her cube shown in three diﬀerent posi ons. Each me adiﬀerent number is facing the front.Can you work out which number is on the opposite faces to these?16E2SERIESTOPICa4b3c1Space, Shape, and PositionCopyright 3P Learning
Painted cubesolveGeƫngreadyMaƟlda built a cube from 27 smaller cubes. She then dipped thelarge cube in blue paint. When it was completely dry, she broke itup into the smaller cubes.Whatto doUse the table below to predict the following:a How many small cubes have three faces covered with paint?b How many small cubes have two faces covered with paint?c How many small cubes have one face covered with paint?d How many small cubes have no faces covered with paint?Number of facescovered in paintNumber ofsmall cubesa38b212c16d01TotalSpace, Shape, and PositionCopyright 3P Learning27E2SERIESTOPIC17
Position – describing positionWhen we use terms such as leŌ and right, where we are in relaƟon to theobject changes.1JoLilyLook carefully at each person’sposiƟon and circle either leŌ or rightin each sentence:a The grapes are on the leŌ / rightof Roger.b The boƩle is on theleŌ / right of Jo.c The sandwiches are onLily’s leŌ / right.d The jug is on Rachel’sleŌ / right.Rogere Jo is siƫng on the leŌ / rightof Lily.Rachelf Roger is siƫng on the leŌ / right of Rachel.2Solve this riddle:What is so fragile that even saying it out loud can break it?ALFSILENCEabcdefgG CH M PIBE O XEJR W SY Na BoƩom row, third column from leŌ.b Third row from boƩom, second column from right.c Top row, second column from leŌ.d Second row from boƩom, first column.e BoƩom row, column on far right.f Top row, column on far right.g Second row from boƩom, first column.18E3SERIESTOPICSpace, Shape, and PositionCopyright 3P Learning
Position – describing position3Write the names of each student according to Miss Flenley’s seaƟng plan:a Josh is in front of Rachel.b Emily is in front rowSimonGinaLynRachelsecond from the right.c Karl is behind Emily.d Liam is in middle row onthe far right.e Bec is on Emily’s leŌ.JoshMeganKarlLiamf Gina is behind Karl.g Megan is between Joshand Karl.h Lyn is on Gina’s leŌ.AndrewJoEmilyBeci Jo is in front of Megan.j Simon is next to Gina.Frontk Andrew is in front of Josh.Here is a map showing the best secret hidingspots in a backyard.4CAA Behind the clothes lineB Behind the garageBC Up the treeDD Around the side of the houseE Next to the recycling binsEWhere are these kids hiding? Write the leƩer.a Ellie is row 2, column 2.Db George is row 1, column 6.Ec Akhil is row 5, column 1.Ad Bri is row 4, column 4.Be Taylor is row 5, column 5.CHint: Row 1 isthe boƩom row.Space, Shape, and PositionCopyright 3P LearningE3SERIESTOPIC19
Position – following directionsupOn this page, you will pracƟse followingthe direcƟons up, down, leŌ and right.leŌrightdown1Three kids are playing a computer game where they have to move through asmany stars as possible to get the most points. Colour each player’s paths accordingto the direcƟons below: AzumiTylerGemmaa Gemma’s path is: Start in the boƩom row; 6th square from the leŌ; 1 up;3 squares leŌ; 6 squares up; and 2 squares leŌ.b Azumi’s path is: Start in the 2nd row from the boƩom on the right;2 squares up; 3 squares leŌ; 2 squares up; 3 squaresright; and 2 squares up.c Tyler’s path is:Start in the boƩom row; 1st square on the right; 2 squares leŌ;2 squares up; 3 squares leŌ; 5 squares up; and 1 square right.d A star is worth 10 points, what was each player’s score?GemmaAzumi3020E3SERIESTOPIC40Space, Shape, and PositionCopyright 3P LearningTyler20
Position – grids and coordinatesMaps are o en set up in a grid with le ers and numbers down the sides.We use these le ers and numbers to pinpoint a par cular part of the map.ASome mes, itis the rows andcolumns thatare labelled.1BCDA1Other mes itis the lines thatare labelled.234BCD1234Answer the quesƟons about what is in each part of the grid.octagona Name the shape at C4.27b Mul ply the number at A2 by 3.pentagonc Name the shape at B2.12 O Q 21293Â4V14d Add the numbers at D1 and A1.À 6T 45AB16ÄC8De What is diﬀerent about the shape at B1 compared with the other shapes in this grid?It’s a circle so it’s not a polygon.2Plot and join the following points. What picture have you made?a D1 to A3, A3 to C3, C3 to C7, C7 to E7,E7 to E3, E3 to G3, G3 to D1.A BC DEFb E1 to D4, D4 to A4, A4 to C6, C6 toB9, B9 to E7, E7 to H9, H9 to G6, G6 to4, 4 to F4, F4 to E1.G HA B1122334455667788C DEFG H9ArrowPicture:StarPicture:Space, Shape, and PositionCopyright 3P LearningE3SERIESTOPIC21
Position – using a mapHere is a map from a street directory. When you learn to drive, you willsomeƟmes use a street directory to find out how to get somewhere.1Look carefully at this map and answer the quesƟons below:10Denison StDenison Ln7Keiran LnNewland St3Stanley St1ABGardiner StStanley LnMackenzie StFitzgerald StCDEFGHIJKLEbley StCuthbert St2Walter StNewland LnNewland StBirrell StNewland LnSampleanswer.Ebley StAlt LnNewland Ln4Newland StLawson StClemenstonPark5Alt LnAlt StKieran St6Birrell StAlt StLawson LnDenison LnCuthbert St8Lawson Ln9MNa Which street is at E4?Newland Lnb What is parallel to Denison Lane at E8?Alt Stc Which street is at J9?Lawson Lnd What are the coordinates that best pinpointthe intersecƟon of Birrell St and Newland St?G5e Draw one way to get from the corner of Lawson St and Ebley St to the corner ofCuthbert and Fitzgerald St.f Describe how to get to Clemenston Park from B8.Sample answer.Goalong Cuthbert St, cross over Alt St and Alt Ln. Turn left atNewlandSt. Cross over Birrell St, pass Kieran St on the left.ClemenstonPark is on the left.22E3SERIESTOPICSpace, Shape, and PositionCopyright 3P Learning
Position – compass directionsWe can use a compass to help us with direcƟon.There are four main points on a compass:N – northS – southE – eastW – westThe points in between the four main points help usdescribe posiƟon more accurately.NW – north westNE – north eastSE – south eastSW – south westNWNEWESWSESOn each compass, some direcƟons are missing. Fill in the missing ones:cEWWNNNSSSEbWaE1N2Here are fourclowns that mustfind their wayto class at circusschool. Write thedirecƟon that eachclown needs togo to get to theirclass in the spacesbelow. Take note ofwhere north is.JugglingNMagic tricksPogoBozoFire twirlingFlying trapezeFace painƟngDimplesAcrobaƟcsSEa Pogo is goingto the acrobaƟcs class.NEb Dimples is goingto the juggling class.TwinklesHint: Use thepoints betweenthe four main points.SWc Bozo is headingto the face painƟng class.NWd Twinkles is headingto the magic tricks class.e Once Twinkles is at the magic tricks class, whichSEdirecƟon will he go to get to the flying trapeze class?Space, Shape, and PositionCopyright 3P LearningE3SERIESTOPIC23
Hit the pointsGeƫngreadyapplyThis is a game for two players. You will need four copiesof this page (two grids for each player) and 10 counters.Whatto doObservestudents.copyEach player places all 10 counters in diﬀerent posi ons on theirgrid without the other player seeing. Take turns to find eachother’s counters by calling out coordinates. The aim of the gameis to find out where all the counters are before the other playerdoes. Don’t waste your guesses. Keep track of your guesses bymarking them on the second grid.ABCDEFGHIJ1242E3SERIESTOPIC3456Space, Shape, and PositionCopyright 3P Learning78910
Look at each group of lines. Trace over any parallel lines with a coloured pencil: Lines, angles and shapes – parallel and perpendicular lines 1 2 3 Parallel lines are always the same distance away from each other at any point and can never meet. They can be any length and go in any direc on. ab c ab c Perpendicular lines meet at right angles.
parallel lines and transversals Use . Auxiliary lines. to find unknown angle measures . Parallel Lines and Angle Pairs . When two parallel lines are cut by a transversal, the following pairs of angles are congruent. corresponding angles alternate interior angles alternate e
- Page 8 Measuring Angles: Real-Life Objects - Page 9 Draw Angles - Page 10 Draw Angles: More Practice - Page 11 Put It All Together: Measure & Draw Angles - Page 12 Joining Angles - Page 13 Joining More Than Two Angles - Page 14 More Practice: Joining Angles - Page 15 Separating Angles .
Sort the following angles into pairs of complementary angles (two angles that have measures that add up to 900) and supplementary angles (two angles that have measures that add up to 180 0 ). WAM 10 Ch.5: Angles & Parallel Lines Extra Notes Handout Page 5
two acute vertical angles . Geometry Unit 2 Note Sheets (Segments, Lines & Angles) 6 Angle Pair Relationships Vertical Angles Complementary Angles Supplementary Angles Linear Pair Guided Practice 5. Find the measures of two supplementary angles if the measures of one angles is 6 less than five t
Adjacent angles are two angles that share a common vertex and side, but have no common interior points. 5 and 6 are adjacent angles 7 and 8 are nonadjacent angles. Notes: Linear Pairs and Vertical Angles Two adjacent angles are a linear pair when Two angles are vertical angles when their noncommon sides are opposite rays.
3 Parallel and Perpendicular Lines Mathematical Thinking: Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. 3.1 Pairs of Lines and Angles 3.2 Parallel Lines and Transversals 3.3 Proofs with Parallel Lines 3.4 Proofs with Perpendicular Lines 3.5 Slopes of Lines 3.6 Equations of Parallel and .
3 Parallel and Perpendicular Lines 3.1 Pairs of Lines and Angles 3.2 Parallel Lines and Transversals 3.3 Proofs with Parallel Lines 3.4 Proofs with Perpendicular Lines 3.5 Equations of Parallel and Perpendicular Lines Tree House (p. 130) Kiteboarding (p. 143) Crosswalk (p. 154) Bike Path (p. 161) Gymnastics (p. 130) Bi
The module scst_user API is de ned in scst_user.h le. 3 IOCTL() functions There are following IOCTL functions aailable.v All of them has one argument. They all, except SCST_USER_REGISTER_DEVICE return 0 for success or -1 in case of error, and errno is set appro-priately. 3.1 SCST_USER_REGISTER_DEVICE