NM Standards GT.A.7

Example 5-1a Determine which lines, if any, are parallel. consecutive interior angles are supplementary. So, consecutive interior angles are not supplementary. So, c is not parallel to a or b. Answer:

Example 5-1b Determine which lines, if any, are parallel. Answer: f || g

Example 5-2a ALGEBRA Find x and m  ZYN so that Explore From the figure, you know that and You also know that are alternate exterior angles.

Example 5-2b Alternate exterior angles Subtract 7x from each side. Substitution Add 25 to each side. Divide each side by 4. Solve Plan For line PQ to be parallel to MN, the alternate exterior angles must be congruent. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find

Example 5-2c Answer: Original equation Simplify. Examine Verify the angle measure by using the value of x to find Since

Example 5-2d ALGEBRA Find x and m  GBA so that Answer: x = 9, Angle = 60°

Example 5-4a Answer:

Example 5-4b Answer: No, the slopes are not the same

More Theorems

Postulate (Rule) If two lines in a plane are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.

Postulate (Rule) If given line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line. There are many lines that can be drawn through Point B, but only one that is parallel to line m

HW: Page 154