1. Definitions
Parallel Lines Two lines are parallel lines if they lie in the same plane and do not intersect.

2. Definitions
Perpendicular Lines Two lines are perpendicular lines if they intersect to form a right angle.

3. Definitions
Skew Lines Two lines are skew lines if they do not lie in the same plane. Skew lines never intersect.

4. Definitions
Converse The converse of an if-then statement is the statement formed by switching the hypothesis and the conclusion. Here is an example. Statement: If two segments are congruent, then the two segments have the same length. Converse: If two segments have the same length, then the two segments are congruent.

5. Theorem 3.1
All right angles are congruent.

6. Theorem 3.2
If two lines are perpendicular, then they intersect to form four right angles.

7. Theorem 3.3
If two lines intersect to form adjacent congruent angles, then the lines are perpendicular. Converse: If two lines are perpendicular, then they form congruent adjacent angles.

8. Theorem 3.4
If two sides of adjacent acute angles are perpendicular, then the angles are complementary.

9. Section 3.4 & 3.5 Parallel lines and Transversals

10. Definitions Transversal:
3.3 Parallel Lines and Transversals
Definitions
Transversal:
Is a line, ray or segment that intersects two or more coplanar lines, rays or segments each at a different point

11. Definitions Alternate Interior Angles
3.3 Parallel Lines and Transversals
Definitions
Alternate Interior Angles
Are two nonadjacent interior angles that lie on opposite sides of a transversal

12. Definitions Alternate Exterior Angles
3.3 Parallel Lines and Transversals
Definitions
Alternate Exterior Angles
Are two nonadjacent exterior angles that lie on opposite sides of a transversal

13. Definitions Same-Side Interior Angles
3.3 Parallel Lines and Transversals
Definitions
Same-Side Interior Angles
Are interior angles that lie on the same side of a transversal

14. Definitions Corresponding Angles
3.3 Parallel Lines and Transversals
Definitions
Corresponding Angles
Are two nonadjacent angles, one interior and one exterior, that lie on the same side of a transversal

15. Alternate interior angles
3.3 Parallel Lines and Transversals
1) Identify pairs of angles.
Corresponding angles
Alternate interior angles
Same-side interior angles
Alternate exterior angles

16. Theorems, Postulates, & Definitions
3.3 Parallel Lines and Transversals
Theorems, Postulates, & Definitions
Corresponding Angles Postulate 8: If two parallel lines are cut by a transversal, then corresponding angles are congruent. .
corresponding angles
2  3

17. Theorems, Postulates, & Definitions
3.3 Parallel Lines and Transversals
Theorems, Postulates, & Definitions
Alternate Interior Angles Theorem 3.3.3:
If two lines cut by a transversal are parallel, then
alternate interior angles are congruent.
alternate interior angles
1  3

18. Theorems, Postulates, & Definitions
3.3 Parallel Lines and Transversals
Theorems, Postulates, & Definitions
Alternate Exterior Angles Theorem 3.3.4:
If two lines cut by a transversal are parallel,
then alternate exterior angles are congruent.
alternate exterior angles
2  5

19. Theorems, Postulates, & Definitions
3.3 Parallel Lines and Transversals
Theorems, Postulates, & Definitions
Same-Side Interior Angles Theorem 3.3.5:
If two lines cut by a transversal are parallel, then
same-side interior angles are supplementary.
same-side interior angles
1 + 4 = 180

20. Theorem 3.12
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.

21. m || n and m1 = 135°. 2) Find angle measures formed by parallel lines
3.3 Parallel Lines and Transversals
2) Find angle measures formed by parallel lines
and transversals.
m || n and m1 = 135°.

22. Given m || n and transversal t Prove: 1  3
3.3 Parallel Lines and Transversals
Given m || n and transversal t
Prove: 1  3