3.8 Constructing Parallel and Perpendicular Lines

1. “Geometry will be important to you later in life because there’s going to be a test six weeks from now.”

2. 3.8 Constructing Parallel and Perpendicular Lines You will construct parallel and perpendicular lines. You will use constructions to explore attributes of geometric figures.

3. First, let’s review how to bisect an angle. Given an angle…

4. First, let’s review how to bisect an angle. Make an arc at the vertex….

5. First, let’s review how to bisect an angle. Go to the intersection of the arc and angle and make an arc.

6. First, let’s review how to bisect an angle. Now, the other intersection and make a arc

7. First, let’s review how to bisect an angle. Connect the intersection & vertex

8. Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Draw a line through the point to the line.

9. Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Make an arc.

10. Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Make another arc.

11. Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Measure the arc.

12. Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Using the measure, make another arc.

13. Now, let’s construct the line parallel to a given line and through a given point that is not on the line. Connect the intersection and the dot

14. Now, you try it with the line and point you were given.

15. How about making a quadrilateral with one pair of parallel sides (a||b). Start off by drawing a point. a b

16. How about making a quadrilateral with one pair of parallel sides (a||b). Measure line b a b

17. Place the compass point on the dot you drew… How about making a quadrilateral with one pair of parallel sides (a||b). and make an arc. a b

18. How about making a quadrilateral with one pair of parallel sides (a||b). Now, draw the segment. a b

19. How about making a quadrilateral with one pair of parallel sides (a||b). Next draw a point not on the line, and connect the two dots. a b

20. How about making a quadrilateral with one pair of parallel sides (a||b). With the compass point on the first dot, create an arc. a b

21. How about making a quadrilateral with one pair of parallel sides (a||b). Repeat the last step with the second dot. a b

22. How about making a quadrilateral with one pair of parallel sides (a||b). Position the compass point halfway between the first arc and the first dot, draw an arc. a b

23. How about making a quadrilateral with one pair of parallel sides (a||b). Repeat the last step with the second dot; draw an arc. a b

24. How about making a quadrilateral with one pair of parallel sides (a||b). Measure line a. a b

25. How about making a quadrilateral with one pair of parallel sides (a||b). Place compass point on the second dot, and draw an arc. a b

26. How about making a quadrilateral with one pair of parallel sides (a||b). Connect the second arc with the second dot passing through the two intersecting arcs. a b

27. How about making a quadrilateral with one pair of parallel sides (a||b). Construct a line on the right side connecting the arc with the line and the lower arc. a b

28. How about making a quadrilateral with one pair of parallel sides (a||b). Do you see the quadrilateral? a b End day 1

29. 3.8 Constructing Parallel and Perpendicular Lines (part deux) You will construct parallel and perpendicular lines. You will use constructions to explore attributes of geometric figures.

30. One last one. Let’s make a line perpendicular to another line going through a point not on the line. Create an arc from the point that cuts the line.

31. One last one. Let’s make a line perpendicular to another line going through a point not on the line. Create an arc from the point that cuts the line.

32. From the intersections make a smaller arc that goes more than a fourth of the way around.

33. Repeat step 3 from the other direction.

34. Next, connect the point with the intersection of the two arcs,

35. Draw a line parallel to the given line through the given point. Bisect the angle. Make quadrilateral with one pair of parallel sides (a||b). Draw a line perpendicular to the given line through the given point a b

36. Perpendicular From a Point to a Line

37. Perpendicular From a Point to a Line

38. Perpendicular to a Point

40. Assignment

41. 3.8 Constructing Parallel and Perpendicular Lines Geometry Draw a line parallel to the given line through the given point. Bisect the angle. Make quadrilateral with one pair of parallel sides (a||b). Draw a line perpendicular to the given line through the given point a b

42. 3.8 Constructing Parallel and Perpendicular Lines Geometry Draw a line parallel to the given line through the given point. { 2 sets} Bisect the angles. {3 angles} Make quadrilateral with one pair of parallel sides (a||b). Draw a line perpendicular to the given line through the given point. { 2 sets} a b

43. 3.8 Constructing Parallel and Perpendicular Lines Geometry Construct a square with side of length a. Construct a rectangle with base a and height b. a a b