1. 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

2. Two nonvertical lines are parallel if and only if they have the same slope.

3. prove that if two lines are parallel, then they have the same slope.
Suppose lines m and n are parallel lines that are neither vertical nor horizontal.
Let A and B be two points on line m, as shown. You can draw a horizontal line through A and a vertical line through B to create the 'slope triangle’ ΔABC.
You can extend AC to intersect line n at point D and then extend it to point F so that AC = DF. Finally, you can draw a vertical line through F intersecting line n at point E.

5. 1. Find the coordinates of the missing vertex in each parallelogram.

6. 2. Find the coordinates of the missing vertex in each parallelogram.

7. 3.

8. 4.