1. 8.1 Bring a Ruler, Protractor and Compass!
Parallel Lines
8.1
Bring a Ruler, Protractor and Compass!

2. Parallel Lines
What is a parallel line? Parallel lines - are lines on the same flat surface that never meet...they are the same distance apart, no matter where you measure.

3. Strategies to Create Parallel Lines
1) Use a Ruler Put a ruler down and strike a line on either side of the ruler. Simulation:

4. Strategies to Create Parallel Lines
2) Use a Protractor
Construct Line Segment AB
Place the protractor on the line segment.
Mark 90° on the paper.
Slide your Protractor 3-4 cm down the line segment and place a second point at 90°.
Connect these two points with a ruler.
Name this new line segment MN
Simulation:

5. Strategies to Create Parallel Lines
3) Use a Compass
Make a line segment with a straight edge. Put a point at each end of this line segment and name these points A and B.
Put 2 points on the line about 4 cm apart. Name these 2 Points D and E.
Place a point (C) above D. Use you compass to make a circle. Do not move the compass width!
Move compass over to E and make a circle
Place compass on E and C. Without moving the width of the compass place the point on D and make another circle.
Mark the point that intersects the two circles and connect C and F together. Extend the line.
Simulation:

6. Homework
Page 302 # *A handout is required to complete question 6. Bring a ruler, triangle, protractor, compass and graph paper.

7. 8.2 Bring a ruler, triangle, protractor, compass and graph paper.
Perpendicular Lines
8.2
Bring a ruler, triangle, protractor, compass and graph paper.

8. Review
Simulation:

9. Investigate
With a partner, complete the following: 1. Draw a line segment (7-8 cm long) on graph paper. 2. Using the tools provided (and your imagination), construct a second line segment perpendicular to the first. Complete 1 and 2 above in as many ways as you can. Try to find (at least) 3 different methods. Simulation:

10. Methods to Construct Perpendicular Lines
What methods were you able to use to make perpendicular lines? 1. Use a plastic triangle (right triangle). 2. Use paper folding. 3. Ruler and a protractor. 4. Use a mira. 5. Use a ruler and a compass.

11. Definition
Perpendicular Line – 2 line segments are perpendicular if they intersect (meet) at a right angle (90 degrees).

12. Ruler and Compass
Simulation:

13. Example 1
List pairs of lines which are perpendicular.

14. Example 2
List pairs of lines which are perpendicular.

15. Homework
Page 305 #1 2b 3 5 Bring a ruler, protractor, and compass.

16. Constructing Perpendicular Bisectors
8.3
Quiz Coming Soon!

17. Review

18. Introduction Video

19. Definition
Bisect - To divide into two equal parts. Perpendicular Bisector - The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment.

20. Strategies for Constructing a Perpendicular Bisector
Paper folding so that point A lies on point B
Using a ruler and a protractor
Use a ruler to measure the length of AB
Mark the midpoint C
Place the centre of the protractor on C; align the base of protractor with AB Mark point D at 90 𝑜
Draw line through CD
Using a Compass and Straight Edge
Simulation:

21. Compass and Ruler
Simulation:

22. Example 1
Construct a perpendicular bisector for line segment AB that is 5 cm long using each of the above methods.

23. Example 2
Construct a perpendicular bisector for line segment AB that is 3.2 cm long using each of the above methods.

24. Homework
Page 308 #1 3-6

25. Constructing Angle Bisectors
8.4

26. Review
Simulation:

27. Introduction Video

28. Definition
Angle Bisector - When you divided an angle into two equal parts.

29. Strategies to Construct Angle Bisectors
1) Paper Folding
Fold xy so that it lies along zy. Crease along the line. The fold line is the bisector of xyz

30. Strategies to Construct Angle Bisectors
2) Protractor and Ruler
Draw an angle
Line the protractor up with one of the lines of the angle. Find the degree of the angle and divide by 2.
Then find that degree on the protractor and mark it.
Draw a line from the vertex of the angle to the point you made.
You now have bisected an angle. Both sides of the bisector should be the same
Simulation:

31. Strategies to Construct Angle Bisectors
3) Compass and Straight Edge
Simulation:

32. Example 1
Bisect an angle that is 122 degrees using each of the above methods.

33. Example 2
Bisect an angle that is 178 degrees using each of the above methods.

34. Homework
Page 312 #

35. Graphing on a Coordinate Grid
8.5
Bring a Ruler and Graph Paper!

36. Investigate (Page 315)

37. Coordinate Plane
A coordinate grid is formed when a horizontal and vertical number line intersect at right angles (0,0). The horizontal line is the x-axis. The vertical number line is the y-axis. The axes are divided in to 4 quadrants numbered 1,2,3,4 counterclockwise starting in the top right quadrant. 2
(-,+) 1
(+,+) 3
(-,-) 4
(+,-)

38. Coordinate Plane
A point on the coordinate grid is located by an ordered pair of numbers.
The first number, the x-coordinate, tells how far left or right of the origin the point is.
The second number, the y-coordinate,
tells how far up or down from the origin
the point is.

39. Example 1 Graph each of the following points: (-2, 6) (4, -7) (-6, -2)
(4, 8)
(0, -16)

40. Example 2
Determine the coordinates of each point on the graph. a) b) c) d) e) A B C D E

41. Example 3

42. Homework
Page 318 #

43. Graphing Translations and Reflections
8.6
Bring a Ruler and Graph Paper!

44. Review

45. Introduction Video

46. Definitions
What is a Translation? Translation - moves (slides) a shape in a straight line. The shape and its image are congruent and have the same orientation. The new object is indicated by putting a ' after each of the points of the object. The ' is referred to as 'prime'.

47. Translation If an object is translated:
Right, it means in the positive direction
Left, it means in the negative direction
(just like in a horizontal number line)
Up, it means in the positive direction
Down, it means in the negative direction
(just like in a vertical number line)

48. Example 1
Plot these points on a coordinate grid: A(1, 6), B(2, 4), C(4, 4), O(0, 0) a) Draw the image of quadrilateral ABCO after a translation 2 units left and 3 units up.

49. Example 2
Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5). a) Translate each point 3 units left and 4 units down to get image points A’, B’, C’. b) Write the coordinates of each point and its translation image. What pattern do you see in the coordinates?

50. Definition
Reflection - creates a mirror image of a shape. The shape and its image are congruent, but have different orientations. The easiest way to figure out a reflection is count the distance the points of the object are from the reflection line.

51. Example 3
Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5). Reflect each point in the x-axis to get image points A’, B’, C’.

52. Example 4
Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5). Reflect each point in the line through (–10, –10) and (10, 10) to get image points A’, B’, C’.

53. Homework
Page 322 #1 2a-c Bring a Ruler, Protractor and Graph Paper!

54. 8.7 Bring a Ruler, Protractor and Graph Paper!
Graphing Rotations
8.7
Bring a Ruler, Protractor and Graph Paper!

55. Review

56. Investigate

57. Investigate (Page 325)

58. Rotations Require 3 things: Turn Center Degree of Rotation
Usually a point, like the origin.
Degree of Rotation
90 degrees, or 270 degrees...
Direction of rotation.
Clockwise(cw or -) or counterclockwise(ccw or +).

59. Constructing a Rotation
Construct the original shape at the given location. Label it.
Trace the original, it's labels, and the x and y axis.
Use a sharp pencil. Push down, through the tracing paper, on the turn center.
While pushing down turn the tracing paper in the desired direction and the required degrees.
Transfer the markings on your tracing paper to your grid.

60. Example 1

61. Example 2
Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5) a) Rotate each point +90 degrees about the origin to get image points A’, B’, C’. b) Write the coordinates of each point and its rotation image.

62. Example 3
Plot these points on a coordinate grid: A(2, 1), B(–1, 2), C(1, 5)
Rotate each point +180 about the origin to get image points A’, B’, C’.
Write the coordinates of each point and its rotation image.

63. Homework
Page 327 #