In this post, I'll explain what are parallel lines, perpendicular lines, and slopes. I'll tell you how to determine the slope of a line and the relation between parallel and perpendicular lines.


3-3 Parallel Lines

41.The Reflexive, Symmetric, and Transitive Properties are true for parallel lines. You can see why in the example below:

Reflexive: AB || CD
Symmetric: If AB || CD, then CD || AB
Transitive: If AB || CD, and CD || EF, then AB || EF.

3-4 Perpendicular Lines

27.

28.The rungs on a ladder are perpendicular to the sides of the ladder. Parallel lines are lines that never intersect if they are extended forever. But the fact that the rungs are all perpendicular to the sides of the ladder helps prove that they are parallel to each other. This can be supported by Theorem 3-4-3.

3-5 Slopes

23. AB > 0-1

24. Lines that represent two cars driving at the same speed would be equal.

2 ways to determine a slope of a line

You can use the following formulas to find the slope of a line:

1.Using the two points' coordinates, you divide the difference of the y-coordinates with the difference of the x-coordinates to find your slope
2. Or use the equation: y=mx+b



The slopes of the lines on the left are the same because they are parallel to each other.
While the slope of the lines on the right, are negative reciprocals of each other because they are perpendicular. Meaning if one line's slope is -2, then the other is 1/2.