1. Geometry Notes
Sections 3-1

2. What you’ll learn
How to identify the relationships between two lines or two planes
How to name angles formed by a pair of lines and a transversal

3. Vocabulary Parallel lines Parallel planes Skew lines Transversal
Interior Angles
Exterior Angles
Consecutive (same – side ) Interior Angles
Alternate Interior Angles
Alternate Exterior Angles
Corresponding Angles

4. RELATIONSHIPS BETWEEN LINES
2 Lines are either
Coplanar
Noncoplanar
The lines intersect once (INTERSECTING LINES)
Two noncoplanar lines that never intersect are called SKEW lines.
The lines never intersect (PARALLEL LINES)
This is what we’ll study in Chapter 3
The lines intersect at all pts (COINCIDENT LINES)

5. Let’s start with any 2 coplanar lines
Any line that intersects two coplanar lines at two different points is called a transversal 2 1 4 3
transversal 6
8 angles are created by two lines and a transversal 5 8 7
4 Interior Angles
3, 4, 5, 6
4 Exterior Angles
1, 2, 7, 8

6. Consecutive Interior Angles
We have two pairs of interior angles on the same side of the transversal called Consecutive Interior Angles or same-side interior angles 2 1 4 3 6 5 8 7
The two pairs of consecutive (same-side) interior:
3 &5 and 4 & 6

7. Alternate Interior Angles
We have two pairs of interior angle on opposite sides of the transversal called Alternate Interior Angles 2 1 4
Alternate
Interior 3
Angles 6 5 8 7
The two pairs of alternate interior angles are:
3 &6 and 4 & 5

8. Alternate Exterior Angles
We have two pairs of exterior angles on opposite sides of the transversal called Alternate Exterior Angles 2 1 4 3 6 5 8 7
The two pairs of Alternate Exterior Angles
1 & 8 and 7 & 2

9. Corresponding Angles
Corresponding Angles are in the same relative position 2 1 4 3 6 5 8 7
There are four pairs of Corresponding Angles
1 & 5, 2 & 6, 3 & 7, and 4 & 8

10. Find an example of each term.
Corresponding angles
Alternate exterior angles
Linear pair of angles
Alternate interior angles
Vertical angles

11. Now if the lines are parallel. . .
All kinds of special things happen. . .
The corresponding angles postulate (remember these are true without question) says. . .
If two parallel lines are cut by a transversal, then the corresponding angles are congruent.
The four pairs of Corresponding Angles are 
1  5
2  6
3  7
4  8 2 1 4 3 6 5 8 7

12. Tell whether each statement is always (A), sometimes (S), or never (N) true.
2 and 6 are supplementary
1  3
m1 ≠ m6
3  8
7 and 8 are supplementary
m5 = m4

13. Find each angle measure.

14. Find each angle measure.

15. Find each angle measure.

17. Determine whether or not l1 ║ l2 , and explain why
Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

18. Determine whether or not l1 ║ l2 , and explain why
Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

19. Determine whether or not l1 ║ l2 , and explain why
Determine whether or not l1 ║ l2 , and explain why. If not enough information is given, write “cannot be determined.”

20. Have you learned
How to identify the relationships between two lines or two planes
How to name angles formed by a pair of lines and a transversal
Assignment: Worksheet 3.1