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

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

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

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

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

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

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

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

25. Place compass point on
the second dot,
How about making a quadrilateral with one pair of parallel sides (a||b).
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. from the other direction.
Repeat step 3
from the other direction.

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

35. Bisect the angle.
Draw a line parallel to the given line through the given point.
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
3.8 Constructing Parallel and Perpendicular Lines
Bisect the angle.
Draw a line parallel to the given line through the given point.
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
3.8 Constructing Parallel and Perpendicular Lines
Bisect the angles. {3 angles}
Draw a line parallel to the given line through the given point. { 2 sets}
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
3.8 Constructing Parallel and Perpendicular Lines
Construct a rectangle with base a and height b.
Construct a square with side of length a. a a b