Unit 5 notes - St John Brebeuf

Apprenticeship and workplace Math 10St.John BrebeufUnit 5:MathematicsAngles and Parallel Lines.DepartmentGoals:In this unit you will learn about how angles are measured andcreated for workplace application and how combinations of anglesand lines can be used to create parallel and non-parallel lines.You will use your mathematical skills and knowledge to:o Measure, draw and describe angleso Estimate the measure of angleso Use certain angles to determine whether 2 lines are parallelo Solve problems involving angles, pairs of angles, parallel,non-parallel, perpendicular and transversal linesKey Terms:AngleAngle measureDegreeParallel linesPerpendicular linestransversalS.Duffy Page 1

Apprenticeship and workplace Math 10St.John BrebeufUnit 5.1:Measuring, Drawing and Estimating Angles.‣ Angle: Two arms that meet at a point called the vertex.Angles are measured in degrees using tools such as aprotractor.armVertexarm‣ True Bearing: The angle measured clockwise between North andan intended path or direction expressed in degreesBearings have 3 digits 090 or 145000 is regarded as North.‣ Angle Measure: The number of degrees between two arms joinedat the vertex.‣ Angle Referent: A common standard of angle measureeg. 90 , 45 , 30 and 22.5 used to estimate angles‣ Drawing Angles: You need the following tools to draw certainangles.Set squareRulerCompass.S.Duffy Page 2

Apprenticeship and workplace Math 10St.John BrebeufExample 1.Use a ruler and compass to create the following anglesa) Draw a 90 angleb) Replicate any existing angle.Solution:a) Follow these steps to draw a 90 angleDraw a line segment and mark where you want your 90 to goPut your compass point at your 90 mark and open slightly.Make 2 arcs at equal distance on either side of your 90markWiden the compass a bit more and place the point at one ofthe new marks and make a small arc. Repeat at the othernew mark so the 2 small arcs intersect.Draw a line segment that goes through the 1 st mark youmade and the intersecting arcs.S.Duffy Page 3

Apprenticeship and workplace Math 10St.John Brebeufb) Follow these steps to replicate any existing angle.Use a compass centered at the vertex of the original angle todraw an arc through both arms.Use a ruler to draw one arm of the new angle.Draw an arc of the same radius and arc length as the one you justdrew on the original angle.Take the compass to the original angle and set it so that its pointand tip of the pencil touch the points where the original arcintersects the sides of the angle.Place the compass point at the intersection of the new arc andarm and draw a small arc through the new one.Use the ruler to draw the other arm through the intersectingarcs.Example 2.Estimate the measure of the angle in thediagram .S.Duffy Page 4

Apprenticeship and workplace Math 10St.John BrebeufSolution:Example 3.Estimate the measure of this angle below:Solution:S.Duffy Page 5

Apprenticeship and workplace Math 10St.John Brebeuf‣ Referents diagrams: Shows angles from 0 o to 360A clock face is a good reference diagram.‣ Complementary angles: 2 angles that add up to 90‣ Supplementary angles: 2 angles that add up to 180Example 4.Sort the following into pairs of complementary and supplementaryangles:42 121 107 31 59 19 48 73Solution:S.Duffy Page 6

Apprenticeship and workplace Math 10St.John BrebeufCompass RoseNWESThe angles in a compass rose are a fraction of 360 and measured in aclockwise direction from the North line.Example 5.a) Determine the true bearing between A and BNBAS.Duffy Page 7

Apprenticeship and workplace Math 10St.John Brebeufb) Determine the bearing of B to ANBASolution:a) Estimate first using the compass rose as e referent and thenmeasure the angle using a protractor.The bearing from A to B isS.Duffy Page 8

Apprenticeship and workplace Math 10St.John Brebeufb) Measure the acute angle and subtract from 360Complete notebook assignment page 184 # 1-6S.Duffy Page 9

Apprenticeship and workplace Math 10St.John BrebeufUnit 5.2: Angle Bisectors and Perpendicular lines.‣ Angle Bisectors: A segment, arm or line that separates 2 halvesof a bisected line.72 is bisected into two 36 angles36 Bisector36Example 1.Accurately bisect an angle like the one shown here.Solution:S.Duffy Page 10

Apprenticeship and workplace Math 10St.John BrebeufDo Activity 5.4 on page 190Complete notebook assignment page 192 # 1-7S.Duffy Page 11

Apprenticeship and workplace Math 10St.John BrebeufUnit 5.3 Non-Parallel Lines and Transversals‣ Vertically Opposite Angles: angles created byintersecting lines that share only a vertex.1 23 4‣ Transversal: A line that intersects 2 or more lines.transversalL 1L 2‣ Corresponding Angles: Angles that occupy the same relativeposition in 2 different sections1 23 45 67 8S.Duffy Page 12

Apprenticeship and workplace Math 10St.John Brebeuf‣ Alternate Interior Angles: Angles in opposite positions between2 lines intersected by a transversal1 23 45 67 8‣ Interior Angles: Interior Angles on the same side of atransversal1 23 45 67 8S.Duffy Page 13

Apprenticeship and workplace Math 10St.John Brebeuf‣ Alternate Exterior Angles: Angles in opposite positions outside2 lines intersected by a transversal1 23 45 67 8‣ Exterior Angles: Exterior Angles on the same side of atransversal.1 23 45 67 8S.Duffy Page 14

Apprenticeship and workplace Math 10St.John BrebeufExample 1.Below is the side diagram of porch that is attached to a house.Roof joist123columnWall4 5floorFor each pair of angles below identify:i) the kind of angle pairii) the parts of the porch that make up the angle pairsa) 1 and 4 b) 3 and 5 c) 1 and 3Solution:a)i)_________________________________________________________________________________________________________ii)________________________________________________________________________________________________________S.Duffy Page 15

Apprenticeship and workplace Math 10St.John Brebeufb)i)_________________________________________________________________________________________________________ii)________________________________________________________________________________________________________c)i)_________________________________________________________________________________________________________ii)________________________________________________________________________________________________________Example 2.An electricity pylon is made up of pairs of linesegments and transversals.The diagram below shows part of a pylon.S.Duffy Page 16

Apprenticeship and workplace Math 10St.John BrebeufCross brace 11Cross brace 32435Cross brace 26The following list contains 3 pairs of angles and the type that eachangle pair is. Determine which 2 parts of the tower make up the mainline segments, and which part that makes up the transversals thatform each of these pairs of angles.a) 3 and 4 are corresponding anglesb) 2 and 5 are alternate interior anglesc) 1 and 6 are exterior angles on the same side of the transversalS.Duffy Page 17

Apprenticeship and workplace Math 10St.John BrebeufSolution:a)_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________b)_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________c)_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Complete notebook assignment page 204 # 1-3S.Duffy Page 18

Apprenticeship and workplace Math 10St.John BrebeufUnit 5.4: Parallel Lines and Transversals.‣ When a transversal cuts through 2 parallel linesCorresponding angles are equal : 1=5; 2=6; 3=7; 4=81 23 45 67 8Alternate interior angles are equal: 3=6; 4=51 23 45 67 8S.Duffy Page 19

Apprenticeship and workplace Math 10St.John BrebeufAlternate exterior angles are equal: 1=8; 2=71 23 45 67 8Interior angles on the same side of a transversaladd up to 180 :3+5=180 4+6=1801 23 45 67 8S.Duffy Page 20

Apprenticeship and workplace Math 10St.John BrebeufExterior angles on the same side of a transversaladd up to 180 : 1+7=180 2+8=1801 23 45 67 8Example 1.Calculate the missing anglesSolution:76bacS.Duffy Page 21

Apprenticeship and workplace Math 10St.John BrebeufExample 2.Calculate the missing angles.Solution: x 110Complete notebook assignment page 214 # 1-7S.Duffy Page 22

Apprenticeship and workplace Math 10St.John BrebeufReflect on your learningNow that you have completed this unit checkto youthe box that appliesRED AMBER GREENI understand all the key terms.I can draw, measure andDescribe angles of variousmeasuresI can determine whether pairsof angles are complementaryor supplementaryI can use referents to estimateangles.I can bisect anglesS.Duffy Page 23

Apprenticeship and workplace Math 10St.John BrebeufI can identify and calculatecorresponding, alternate interiorand alternate exterior anglesaround transversalsI can determine whether linesare parallel or notI have completed allhomework assignments.I have attended lunchtimetutorials for extra help.I am ready to sit myunit 5 test.Target:In my Unit Test I hope to achieve%Student’s Signature ____________________Date__________S.Duffy Page 24