# Plane Figures: Two Straight Lines Crossed by a Transversal

## Contents

6-9.

### Materials

• Box of sticks
• Supplies
• Board covered with paper

### Presentation

1. Place one, then another like stick on the board, having the child identify the number of straight lines on the plane.
2. Then place a third stick (a different color with holes along the length) so that it crosses the other two.
3. Now there are three straight lines on our plane; the third crosses the other two.
4. Remove the sticks.
5. Place one horizontally and tack it down reminding the child that this straight line goes on in both directions to infinity.
6. Into how many parts does it divide the plane? Indicate these two parts with a sweeping hand.
7. Place the second stick on the plane so that it is not parallel.
8. Even this straight line goes on to infinity.
9. With a black crayon, draw lines to demonstrate this.
10. Identify the three parts into which the plane has been divided.
11. The part of the plane which is enclosed by the two straight lines is called the internal part which we can shade in red.
12. Above and below the straight lines are the external parts of the plane because they are not enclosed by these two lines.
13. Place the third stick across the other two and tack it down where it intersects.
14. This is a transversal (transversal < transverse: Latin trans, across, and versus, turned; thus lying crosswise).
15. Two straight lines cut buy a transversal on a plane will determine a certain number of angles - how many?
16. Using non-red or non-blue tacks, identify and count the angles.
17. First conclusion: Two straight lines cut by a transversal will form eight angles.
18. Some of these angles are lying in the internal part of the plane, while others are lying in the external part.
19. Remove the tacks.
20.  Identify and count the angles in the internal part, using red tacks (same color as the plane).
21. These four angles are interior angles because they lie in the internal part of the plane.
22. Do the same, identifying the exterior angles.
23. The four angles are exterior angles because they lie in the external part of the plane.

Second presentation:

Two straight lines cut by a transversal form four interior and four exterior angles.

1. We need to divide these eight angles according to different criteria.
2. Remove the red and blue tacks and identify two new groups using two other colors: four angles formed by one straight line and a transversal; and four angles formed by the other straight line and a transversal.
3. All of the work that we'll be doing involves pairing an angle from one group with an angle from another group.
4. We won't be working with two angles from the same group because that would mean only two straight lines were being considered, not three.
5. Let's examine these pairs.
6. Remove the tacks.
7. Using two tacks of the same color, the teacher identifies two angles.
8. These two angles are a pair of alternate angles.
9. Recall the meaning of alternate.
10. One is on one side; the other is on the the other side of the transversal.
11. On what part of the plane are they? Internal, therefore they are also interior angles.
12. We combine these two characteristics into one name: alternate interior angles.
13. Invite the child to identify the other pair with two tacks of a different color.
14. The child draws these and labels them.
15. Remove the tacks.
16. The directress identifies another pair of angles.
17. These are a pair of angles that lie on the same side of the transversal.
18. On what part of the plane do they lie? Internal, therefore they are also interior angles.
19. We can call these interior angles that lie on the same side of the transversal.
20. Invite the child to identify another pair with two tacks of a different color.
21. The child draws the angles and labels them appropriately.
22. Remove the tacks.
23. The directress identifies another pair of angles.
24. These are alternate angles because they lie on on one side one on the other side of the transversal.
25. The child identifies in what part of the plane they lie - external - and their corresponding name - exterior.
26. These are alternate exterior angles.
27. Invite the child to look for another pair and identify them with two tacks of a different color.
28. The child draws the situation and labels it accordingly.
29. Remove the tacks.
30. The directress identifies two angles.
31. These are a pair of angles that lie on the same side of the transversal.
32. The child identifies in which part of the plane they lie - external - and recalls their subsequent name - exterior.
33. Therefore these angles can be called exterior angles that lie on the same side of the transversal.
34. The child is invited to identify another pair using two tacks of a different color.
35. The child copies this situation and labels it.
36. Remove the tacks.
37. This time an exterior angle will be paired in a relationship with an interior angle.
38. The child chooses an angle, identifying it with a tack.
39. The other angle must be formed by the other straight line, as you remember, so that three lines will be involved.
40. The directress identifies the other angle of the pair.
41. These are corresponding angles, because they follow a certain order.
42. Both angles lie on the same side of the transversal, and each angle lies above its straight line.
43. Invite the child to identify other pairs using different color tacks for each pair of angles.
44. All eight angles are used.
45. The child copies the situation and labels it accordingly.
46. Note: These angles have only one quality, since the pair is divided among the two different parts of the plane.
47. Finish with classified nomenclature and commands.
48. A command might ask the child to identify the other member of a given pair of angles.