1. Lesson 3.1 Parallel Lines and Transversals
Students will be able to describe angles formed by parallel lines and transversals

2. Youtube

3. Answer these questions in your notebook:
What does it mean for two lines to be parallel? What are some properties of two parallel lines?

4. When an object is transverse, it is lying or extending across something.
How many angles are formed by the parallel lines and the transversal? Label the angles.
Which of these angles have equal measures? Explain your reasoning. 1 2 4 3 6 5 8 7
Transversal line

5. Transversal: a line that intersect two or more lines
Transversal: a line that intersect two or more lines. When parallel lines are cut by a transversal, several pairs of congruent angles are formed.

6. The measurement of a straight line is 180 degrees.

7. Because of the corresponding angles postulate
PROPERTIES OF PARALLEL LINES
POSTULATE
POSTULATE 15 Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2
Because of the corresponding angles postulate

8. 1 3 2 4 7 5 8 6

9. Because of the alternate interior angles postulate
PROPERTIES OF PARALLEL LINES
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.4 Alternate Interior Angles
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4
Because of the alternate interior angles postulate

11. Because of the alternate exterior angles postulate
PROPERTIES OF PARALLEL LINES
THEOREMS ABOUT PARALLEL LINES
THEOREM 3.6 Alternate Exterior Angles
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. 7 8
Because of the alternate exterior angles postulate

13. j k PROPERTIES OF PARALLEL LINES THEOREMS ABOUT PARALLEL LINES
THEOREM 3.7 Perpendicular Transversal
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other.
j k

14. Key Concepts
Angles can be labeled with one point at the vertex, three points with the vertex point in the middle, or with numbers. See the examples that follow.
1.8.1: Proving the Vertical Angles Theorem

15. Key Concepts, continued
Adjacent angles
∠ABC is adjacent to ∠CBD. They share vertex B and
∠ABC and ∠CBD have no common interior points.
1.8.1: Proving the Vertical Angles Theorem

16. Key Concepts, continued (continued)
Nonadjacent angles
∠ABE is not adjacent to ∠FCD.
They do not have a common vertex.
1.8.1: Proving the Vertical Angles Theorem

17. Key Concepts, continued
Nonadjacent angles
∠PQS is not adjacent to ∠PQR. They share common interior points within ∠PQS.
1.8.1: Proving the Vertical Angles Theorem

18. Key Concepts, continued
Linear pair
∠ABC and ∠CBD are a linear pair. They are adjacent angles with non-shared sides, creating a straight angle.
1.8.1: Proving the Vertical Angles Theorem

19. Key Concepts, continued
Not a linear pair
∠ABE and ∠FCD are not
a linear pair. They are not
adjacent angles.
1.8.1: Proving the Vertical Angles Theorem

20. Vertical angles are nonadjacent angles formed by two pairs of opposite rays. Opposite angles are congruent to each other.
1.8.1: Proving the Vertical Angles Theorem

21. Key Concepts, continued
Vertical angles
∠ABC and ∠EBD are vertical angles.
∠ABE and ∠CBD are vertical angles.
1.8.1: Proving the Vertical Angles Theorem

22. Key Concepts, continued
Not vertical angles
∠ABC and ∠EBD are not vertical angles and are not opposite rays. They do not form one straight line.
1.8.1: Proving the Vertical Angles Theorem

23. Key Concepts, continued
Theorem
Supplementary Theorem
If two angles add up to be 180 degrees, then they are supplementary.
1.8.1: Proving the Vertical Angles Theorem

24. Key Concepts, continued
Complementary angles are two angles whose sum is 90º. Complementary angles can form a right angle or be nonadjacent.
1.8.1: Proving the Vertical Angles Theorem