Question

which statement best explains the relationship between lines cd and fg? they are perpendicular because their slopes are equal. they are perpendicular because their slopes are negative reciprocals. they are not perpendicular because their slopes are equal. they are not perpendicular because their slopes are negative reciprocals.

Explanation:

Step1: Recall slope - perpendicularity relationship

Two lines are perpendicular if and only if the product of their slopes is - 1, which means their slopes are negative reciprocals of each other. Two lines are parallel if their slopes are equal.

Step2: Analyze the given statements

The first statement "They are perpendicular because their slopes are equal" is incorrect since equal - slope lines are parallel. The second statement "They are perpendicular because their slopes are negative reciprocals" would be correct if the lines were perpendicular. The third statement "They are not perpendicular because their slopes are equal" is incorrect as equal - slope lines are parallel, not perpendicular. The fourth statement "They are not perpendicular because their slopes are negative reciprocals" is incorrect because negative - reciprocal slopes indicate perpendicular lines.

Answer:

They are not perpendicular because their slopes are not negative reciprocals. (None of the given options are completely correct based on the correct logic, but the correct concept is that perpendicular lines have negative - reciprocal slopes). If we assume there is a mis - typing in the options and we go with the correct principle, the correct statement should be: They are not perpendicular because their slopes are not negative reciprocals.