1. 3-1 Lines and Angles
3-2 Angles Formed by Parallel Lines and Transversals
3-3 Proving Lines Parallel
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane

2. 3-1 Lines and Angles
Parallel Lines (||): Coplanar lines that do not intersect.
Perpendicular Lines: ( ): Lines that intersect in a 90 degree angle.

3. 3-1 Lines and Angles
Skew Lines: Not coplanar. Neither parallel and do not intersect
Parallel Planes: planes that do not intersect.

4. 3-1 Lines and Angles
Transversal: line that intersects two or more coplanar lines in different points. h k t
Two coplanar lines
Transversal- the line of intersection

5. 3-1 Lines and Angles Interior Angles- Angles 3, 4, 5, 6 h k t 1 2 3 47 8
Exterior Angles-
Angles 1, 2, 7, 8

6. 3-1 Lines and Angles Same side interior angles: ∠3 and ∠5, ∠4 and ∠6 1h k t 1 2 3 4 5 6 7 8
Alternate interior angles:
∠3 and ∠6, ∠4 and ∠5
Alternate exterior angles:
∠2 and ∠7, ∠1 and ∠8
CABRI activity for problems P76 (18-21)
Corresponding Angles
∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

7. 3-1 Lines and Angles
3-2 Angles Formed by Parallel Lines and Transversals
3-3 Proving Lines Parallel
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane

8. 3-2 Angles Formed by Parallel Lines and Transversals
Postulate 3-2-1: Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. k n t

9. 3-2 Angles Formed by Parallel Lines and Transversals
Theorem 3-2-2: Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then alternate interiors angles are congruent. k n t

10. 3-2 Angles Formed by Parallel Lines and Transversals
Theorem 3-2-3: Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. k n t

11. 3-2 Angles Formed by Parallel Lines and Transversals
Theorem 3-2-4: Same-Side Interior Angles Theorem
If two parallel lines are cut by a transversal, then same side interior angles are supplementary. k n t

12. 3-1 Lines and Angles
3-2 Angles Formed by Parallel Lines and Transversals
3-3 Proving Lines Parallel
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane

13. 3-3 Proving Lines Parallel
Theorems: Write the converse of each of the four if-then statements we created last period.
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
If two parallel lines are cut by a transversal, then alternate interiors angles are congruent.
If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.
If two parallel lines are cut by a transversal, then same side interior angles are supplementary.
What do these things mean to you?
This is how we SHOW that any two lines could be/are parallel.

14. 3-1 Lines and Angles
3-2 Angles Formed by Parallel Lines and Transversals
3-3 Proving Lines Parallel
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane

15. 3-4 Perpendicular Lines
Perpendicular Bisector: a line or segment that is perpendicular and goes through the midpoint of a segment. A B

16. 3-4 Perpendicular Lines
Construction: Perpendicular through a point outside the line. X
Distance from point to a line is the perpendicular distance. C D

17. Conditional Statement
3-4 Perpendicular Lines
Write an If-then statement based on info in the table.
Hypothesis
Conclusion
Conditional Statement
3.4.1 If two intersecting lines form a linear pair of congruent angles, then the lines are perpendicular.
3.4.2 In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.
3.4.3 If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

18. 3-4 Perpendicular Lines
Theorem 3-4-1: If two intersecting lines form congruent angles, then the lines are perpendicular.

19. 3-4 Perpendicular Lines
Theorem 3-4-2: In a plane, if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line.

20. 3-4 Perpendicular Lines
Theorem 3-4-3: If two coplanar lines are perpendicular to the same line, then the two lines are parallel.

21. 3-1 Lines and Angles
3-2 Angles Formed by Parallel Lines and Transversals
3-3 Proving Lines Parallel
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane

22. 3-5 Slopes of Lines Slope : steepness of a line
Find the slope between the
points (5,4) and (-7, -3)

23. 3-5 Slopes of Lines
When is slope Positive, Negative, Zero, or Undefined?

24. 3-5 Slopes of Lines
Lines are parallel if their slopes are _______________

25. 3-5 Slopes of Lines
Lines are perpendicular if their slopes _____________

26. 3-1 Lines and Angles
3-2 Angles Formed by Parallel Lines and Transversals
3-3 Proving Lines Parallel
3-4 Perpendicular Lines
3-5 Slopes of Lines
3-6 Lines in the Coordinate Plane

27. 3-6 Lines in the Coordinate PlaneY
How do we identify one line from another line?
The equation of a line helps us identify different types of lines. X

28. 3-6 Lines in the Coordinate Plane
Slope 70 60 50 40
slope = 10 30 20 10 1 2 3 4 5

29. 3-6 Lines in the Coordinate Plane
Point Slope Form
y – y1 = m(x - x1) 70 60 50 40
y - 30 = 10 (x - 1) 30 20 10 1 2 3 4 5

30. 3-6 Lines in the Coordinate Plane
Slope – intercept Form
y = mx + b 70 60 50 40
y = 10x + 20 30 20 10 1 2 3 4 5

31. 3-6 Lines in the Coordinate Plane
A line with slope 3, that goes through (3, -4) in point-slope form.
y + 4 = 3 (x -3)

32. 3-6 Lines in the Coordinate Plane
A line through (-1,0) and (1,2) in slope-intercept form.
y = x + 1

33. 3-6 Lines in the Coordinate Plane
A line with x – intercept at 2 and y – intercept 3 in point- slope form.
y = -3/2 x + 3