UN I T Geometry

G5 U3 & XS2 (78-111) F1 9/7/04 4:04 PM Page 934. Make a large copy of this Venn diagram.Sort the figures.Has a right angleHas an obtuse angleABDCEFHas an acute angleHGIExplain how you know where to place each figure.5. Use a geoboard or square dot paper.Make polygons that have:a) exactly 2 obtuse anglesb) no more than 3 acute anglesc) more than 1 right angled) 1 acute, 1 obtuse, and 1 right angleHow many different polygons can you make in each case?Name each polygon.6. Is it possible for a triangle to have:a) more than 1 obtuse angle?b) 2 right angles?c) 3 acute angles?Explain your thinking.Use pictures and words.ayDyreEvsrebNumNumber StrategiesOrder the numbers in each set fromgreatest to least.How can you use angles to sort polygons?Use pictures, numbers, and words to explain. 1284, 4182, 1428, 1248, 2148 9090, 9009, 9990, 9099, 999 6789, 7689, 6897, 6987, 7869ASSESSMENT FOCUSQuestion 593

G5 U3 & XS2 (78-111) F1 9/7/04 4:06 PM Page 94L E S S O NConstructing TrianglesThese triangles come with a geometry set.The measure of each angle is shown.60 90 30 90 45 You will need: a millimetre ruler triangles from a geometry set Construct triangle DEF.The measure of D is 30 .The measure of E is 60 .The measure of F is 90 .Which side will be the longest?Try to make more thanone triangle DEF. Construct triangle ABC.The length of AB is 66 mm.The measure of A is 120 .The length of AC is 66 mm.How long is side BC?What are the measures of B and C? Name each triangle 2 ways.Record your work.94LESSON FOCUSConstruct triangles given side and angle measures.45

G5 U3 & XS2 (78-111) F1 9/7/04 4:06 PM Page 95S h o w and S h a r eCompare your triangles with those of another pair of students.Is it possible to make different triangles ABC? DEF? Explain.You can use a ruler and a protractor to construct a triangle.Construct triangle MNP.The length of MN is 4.5 cm.The measure of M is 40 .The length of MP is 3.7 cm.Step 1Sketch the triangle first.Label each side and angle.This sketch is not accurate.It shows each given measure.Step 2Use a ruler to draw side MN4.5 cm long.012345678Step 3Place the protractor on MN,with its centre at M.From 0 on the inner circle,measure an angle of 40 at M.95

G5 U3 & XS2 (78-111) F1 9/7/04 4:06 PM Page 9687Step 4Remove the protractor.Join M to the mark at 40 .Measure 3.7 cm from M.Mark the point P.6543210Step 5Use a ruler to join P to Nto form side NP.Label the triangle with its measures.1. Use a ruler and a protractor.Construct each triangle.Sketch the triangle first.a) Triangle RSTThe length of side TS is 5.2 cm.The measure of T is 26 .The length of side RT is 3.4 cm.b) Triangle VWXThe length of side VW is 7 cm.The measure of V is 60 .The measure of W is 50 .Label each triangle with the measuresof all the sides and angles.2. Use a geoboard or dot paper.Construct a triangle with two 45 angles.Do this 3 times to construct 3 different triangles.How are the triangles the same? Different?96ayDyreEvsrebNumNumber StrategiesUse addition, subtraction,multiplication, or division.Find 10 different ways tomake 42.

G5 U3 & XS2 (78-111) F1 9/7/04 4:06 PM Page 973. Use a ruler and a protractor.Construct a triangle with angles 40 , 60 , and 80 .Compare your triangle with that of a classmate.Are your triangles congruent?How could you find out?4. Construct triangle GHK.The measure of H is 45 .The length of side HK is 64 mm.The length of side HG is 46 mm.a) What is the measure of K?What is the length of side GK?b) Suppose the length of side HG is 7 cm.What happens to the measure of K?What happens to the length of GK?Show your work.5. Construct a right triangle with two angles of 55 and 35 .Can you make more than one triangle? Explain.6. Try to construct triangle ABC.Draw AB 42 mm long.The measure of A is 90 .The measure of B is 95 .Can you construct triangle ABC?How do you know?7. Can you construct a triangle with three 45 angles?Explain your thinking.Which measures do you need to knowto be able to draw a triangle?For each example,draw the triangle.ASSESSMENT FOCUSQuestion 4Look for triangles in your home.They could be pictures orobjects with triangular faces.Name each triangle 2 ways.Choose 1 triangle. Draw it.97

G5 U3 & XS2 (78-111) F1 9/7/04 4:08 PM Page 98L E S S O NMaking NetsYou will need: a pyramid tape a millimetreruler scissorsLabel each face of the solid with a letter. Trace each face of the solid.Label each tracing with its letter. Cut out your tracings.Tape them together at the edgesto make a figure.Arrange the faces so the figure can befolded to make a model of your solid.How many different ways can you do this? Fold the figure to build the model.ayDyres EvrebmNuNumber StrategiesWrite each number as a decimal. one and one-hundredth twelve and twelve-hundredthsS h o w and S h a r eShare your work with another pair of students.How did you decide how to arrange the faces?98LESSON FOCUSIdentify and construct nets of solids. three hundred three andthree-tenths four hundred forty andfour-hundredths

G5 U3 & XS2 (78-111) F1 14/7/04 11:17 AM Page 99A net shows all the faces of a solid, joined in one piece.It can be folded to form the solid.Here are 2 ways to construct a net for a solid. Construct a net for this cube. The cube is a cardboard carton.Carefully cut the cube apart along its edges so it is in one flat piece. Construct a net for this triangular pyramid.Label each face of the solid.Faces A and Bform one edge.I will draw faces A and Bso they share one side.Trace one face.ATrace each other face.Arrange the faces so when they are folded,they make the pyramid.BDAC99

G5 U3 & XS2 (78-111) F1 9/7/04 4:08 PM Page 100You will need a variety of solids.1. Identify each solid.How many faces does it have?Sketch each face.a)b)c)d)2. Choose 2 solids.Make sure the solids are different from the solidin Explore.Construct a net for each solid.3. Which solid would each net make?How do you know?a)b)c)d)100

G5 U3 & XS2 (78-111) F1 9/7/04 4:08 PM Page 1014. Which diagrams show nets?Identify the solid.If a diagram does not show a net, how could you change it to make a net?a)b)c)d)5. The net for a cube has 6 congruent squares.a) How many different ways can you arrange6 squares to form a net for a cube?Record each way on grid paper.b) How do you know each arrangement forms a net?Show your work.6. Identify each solid.a) It has 6 congruent square faces.b) The faces are 2 congruent trianglesand 3 congruent rectangles.c) The faces are 3 pairs of congruent rectangles.d) Two faces are congruent hexagonsand 6 faces are congruent rectangles.How can you tell if an arrangement of figures is a net?Use words and pictures to explain.ASSESSMENT FOCUSQuestion 5101

HN OLOGUsing a Computer to Explore NetsYTECG5 U3 & XS2 (78-111) F1 9/7/04 4:51 PM Page 102Work with a partner.Use AppleWorks.Follow these steps to create a net for a cube.1. Open a new drawing document in AppleWorks. Click:2. If a grid appears on the screen, go to Step 3.If not, click:, then click:3. Check that Autogrid is on. Click:If Turn Autogrid Off appears in the menu, Autogrid is on.If not, click:4. Check the ruler settings. Click:Click:, then click:Choose these settings:Click:5. To draw a square, click the Rectangle Tool:The cursor will look like this:Hold down the Shift key while you clickand hold down the mouse button.Drag the cursor. Release the mouse button.102LESSON FOCUSUse a computer to create nets.

G5 U3 & XS2 (78-111) F1 9/7/04 4:52 PM Page 1036. To change the size of the square, click the square to select it.Click:Then click:Enter 6 cm for the width and 6 cm for the height.Click:. This closes the Object Size box.7. To move a square, click the square.Click and hold down the mouse button.Drag the square to where you want it.Release the mouse button.8. To copy a square, click the square.Click:, then click:Click:, then click:The copy shows on top of the square.Click and drag the square to where you want it.9. Follow Steps 5 to 8 to create squares.Then arrange them to form a net for a cube.10. Save your net.Click:, then click:Name your file, then click:11. Print your net.Click:, then click:Click:103

G5 U3 & XS2 (78-111) F1 9/7/04 4:52 PM Page 104Follow these steps to create a net for a square pyramid.12. Repeat Steps 5 to 7 to draw a square.13. To draw a triangle, click the Regular Polygon tool:Click:, then click:Enter 3 for Number of sides. Click:The cursor will look like this:Click one of the vertices of the square.Drag along the edge to another vertex to make a triangle.Release the mouse button.Do this three more times.14. To change the size or shape of the triangle, click the triangleto select it.Click a black square, hold down the mouse button, and draguntil the triangle is the size and shape you want.How did you decide how to arrange the squares to makea net for a cube?Use words and pictures to explain.104

amesWhat’s My Rule?GG5 U3 & XS2 (78-111) F1 9/7/04 4:52 PM Page 105You will need a set of What’s My Rule? game cards,scissors, 2 labels, and two 1-m lengths of string.Cut out the game cards.Spread them out, face up.Use the string to make2 loops.Label one loop “Matches”and one loop “Discards.” Player A thinks of asecret rule thatdescribes someof the polygonson the cards.The rule could be: all triangles with aright angle; or all regular polygons; or all quadrilaterals with 1 pair of parallel sides Player A chooses 2 game cards.One card must fit the rule.He places it face up inside the “Matches” loop.The other card must not fit the rule.He places it face up in the “Discards” loop. Player B chooses a game card.If she thinks the card fits the rule, she places it inside the “Matches” loop.Otherwise, she places it in the “Discards” loop. Player A tells Player B whether her placement is correct.If the placement is correct, she can guess the rule.If the placement is not correct, she cannot make a guess. Players C and D continue until someone guesses the secret rule. Switch roles. Another player thinks of a secret rule.The other players take turns trying to guess the new rule.The winner takes the fewest turns to guess the rule.105

G5 U3 & XS2 (78-111) F1 9/7/04 4:09 PM Page 106hat You KnowWwohSLESSON11. Name each triangle as scalene, isosceles, or equilateral.Tell how you know.MJCKDLHB2N2. Measure the angles in the triangles in question 1.Order the angles from least to greatest.3. Use a protractor.Draw an angle with each measure.a) 65 b) 135 c) 95 Name each angle as acute, obtuse, or right.144. Name each triangle 2 ways.How did you choose each name?VYRSZUXWT45. Is it possible to draw a quadrilateral with:a) 2 obtuse angles?b) 3 obtuse angles?Use pictures and words to explain.6. Is a rhombus a regular polygon?How do you know?106Use dot paper to drawthe quadrilaterals.

G5 U3 & XS2 (78-111) F1 9/7/04 4:09 PM Page 107LESSON57. Use a ruler and a protractor.a) Construct triangle ABC.The length of AB is 56 mm.The measure of A is 35 .The measure of B is 90 .b) What are the lengths of AC and BC?What is the measure of C?8. Try to construct triangle QRS.Draw QR 5 cm long.The measure of Q is 110 .The measure of R is 75 .Can you construct triangle QRS? How do you know?69. Which arrangements of figures show a net for a rectangular prism?How do you know?a)b)IUN TLearnin c) g Goalssort and name polygonsby sides and anglesmeasure, name, andconstruct anglesconstruct triangles, given sideand angle measuresidentify and constructnets of solids107

G5 U3 & XS2 (78-111) F1 9/7/04 4:09 PM Page 108BridgesYou will need: Bristol board a hole punchor a compass paper fasteners a centimetre ruler centimetre cubesor standard massesPart 1Choose one type ofbridge truss to build.Your bridge must: span a 35-cm gap support a load stand up by itselfYour teacher will give you a copy of the truss pieces.Use the truss pieces to cut strips of Bristol board.How many of each size of strip do you need?Cut a strip of Bristol board 14 cm widefor the roadway.How long does the road need to be?Draw a line 2 cm in from each long edge.Fold along the lines.Build the bridge.How will you brace the top?108Pratt TrussDouble Warren Truss

G5 U3 & XS2 (78-111) F1 9/7/04 4:10 PM Page 109istC h e ck LPart 2Look at your bridge.Identify as many of these attributes as you can: congruent figures scalene, equilateral, and isosceles triangles obtuse, acute, and right angles equal anglesName different polygons you see.Are any of them regular? Explain.Your work should showa clear explanation of whatyou did and whyas many attributesas possiblehow you used what youknow about geometryhow you found the greatestmass your bridge couldsupport Part 3Use two desks or some textbooksto make a 35-cm gap.Place your bridge across the gap.Find the load your bridge can support.Compare your bridge with those of other groups.Which type of bridge can support the greatest mass?Write about the bridges and the attributes that make them strong.Howe TrussHowe Truss with counter bracesHow can you use what you know about trianglesand other polygons to draw nets of solids? identify solids from their nets?109

G5 U3 & XS2 (78-111) F1 9/7/04 4:11 PM Page 110Triangle, Triangle, TriangleYou will need a ruler, several sheets of grid paper, and scissors.Part 1 On grid paper, draw a largeright triangle. Make sure its baseis along a grid line and the thirdvertex is at a grid point.Estimate the area of the triangle. On another sheet of grid paper,draw a congruent triangle. Cut out both triangles.Place the triangles edge to edgeto make a rectangle. Write a multiplication statementto find the area of the rectangle.Calculate the area of the rectangle.Compare the area of therectangle to the areaof the triangle.110FOCUSCross Strand Performance Assessment

G5 U3 & XS2 (78-111) F1 9/7/04 4:11 PM Page 111Part 2 Draw a large acute trianglewith its base along a grid lineand the third vertex at agrid point.Estimate the areaof the triangle. Draw a congruent triangle. Cut out both triangles.Then, cut along a grid lineon each triangle to make2 triangles. Arrange the 4 trianglesedge to edge to makea rectangle with no gapsor overlaps. Write a multiplicationstatement to find thearea of the rectangle.Calculate the area of theoriginal acute triangle.Display Your WorkCreate a summary of your work.Show all your calculations. Explain your thinking.Take It Further Draw an obtuse triangle on grid paper.Predict its area. How did you use what you learned about acute andright triangles to make your prediction? Find a way to check your prediction.111

Triangle ABC has 3 sides: AB, AC, and BC Name triangles by the number of equal sides. A triangle has 3 sides. A pentagon has 5 sides. A hexagon has 6 sides. An octagon has 8 sides. An equilateral triangle has all sides equal. An isosceles triangle has 2 sides equal. A scalene triangle has no sides equal. AB BC AC DE DF A B C M QP N A C B .