1. Chapter 3 Parallel and Perpendicular Lines

2. 3-2 Angles Formed by Parallel Lines and Transversals

3. Definitions
Transversal Line: A line that cuts across two or more (usually parallel) lines
Alternate-Interior Where a transversal crosses two (usually parallel) lines. Each pair of these angles are inside the parallel lines, and on opposite sides of the transversal
Alternate-Exterior Angles: Where a transversal crosses two (usually parallel) lines. Each pair of these angles are outside the parallel lines, and on opposite sides of the transversal
Same-Side Interior Angles: where a transversal crosses two (usually parallel) lines. Each pair of interior angles are inside the parallel lines, and on the same side of the transversal
Corresponding Angles: angles that occupy the same relative position at each intersection where a straight line crosses two others. If the two lines are parallel, the corresponding angles are equal.

4. Characteristics

5. Examples in real life

6. 3-3 Proving Lines Parallel

7. Definition
If two parallel lines (p) are cut by a transversal, then the pairs of same side interior angles are supplementary (q).
Converse.
Also if 2 lines are cut by a transversal so that a pair of same side interior angles are supplementary (q), then the lines will come out to be parallel (p).

8. Characteristics
If corresponding angles are congruent, then lines are parallel.
If alternate-interior angles are congruent, then lines are parallel.
If alternate-exterior angles are congruent, then lines are parallel.
If same-side interior angles are supplementary, then lines are parallel.

9. Examples in real life

10. 3-4 Perpendicular Lines

11. Definition
A line is perpendicular to another if it meets or crosses it at right angles (90°).
Perpendicular means “at right angle”. A line meeting another at the right angle, or 90° is said to be perpendicular to it.

12. Characteristics Its part of a parallel line.
Perpendicular lines cross to form 90° angles at the intersection.
If two non-vertical lines in the same plane intersect at a right angle then they are said to be perpendicular.

13. Examples in real life

14. 3-5 Slopes of Lines
By “Lady Mutombo”

15. Definitions
The slope of a line is a number that shows/determines how steep it is.
Slope – A surface of which one end or side is higher than another; a rising or falling surface
Line - A long, narrow mark that never ends

16. Characteristics
(X1, Y1) & (X2, Y2)
Formula : M= (Y2 – Y1)/(X2 – X1)

17. Examples in real life
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18. 3-6 Slopes of Parallel and Perpendicular Lines

19. Definitions
Slope of Parallel Lines: Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel. Perpendicular lines are a bit more complicated.
- Slope of Perpendicular Lines: Lines whose slopes are negative reciprocals of one another. The lines intersect to form right angles. Negative reciprocals are two numbers that when they are multiplied together have product of -1.

20. Characteristics Parallel Lines have same slopes
Perpendicular lines have slopes that are opposite reciprocals

21. Examples in real life

22. Chapter 3
Class Activity

23. Draw parallel and perpendicular lines to a given line
Draw parallel and perpendicular lines to a given line. Find slope and write equation for each line.