Which of the following facts, if true, would allow you to prove that lines l and m are parallel?
Two horizontal lines are shown and they are labeled l and m. They are cut by a transversal. The transversal intersects line l at the top of the image, creating four angles labeled 1, 2, 3, and 4. Angle 1 is in the top left corner. Angle 2 is in the top right corner. Angle 3 is in the bottom left corner. Angle 4 is in the bottom right corner. The transversal intersects line m at the bottom of the image, creating four angles labeled 5, 6, 7, and 8. Angle 5 is in the top left corner. Angle 6 is in the top right corner. Angle 7 is in the bottom left corner. Angle 8 is in the bottom right corner.Angle 1 is above line l and to the left of the intersecting line.
Angle 2 is above line l and to the right of the intersecting line.
Angle 3 is below line l and to the left of the intersecting line.
Angle 4 is below line l and to the right of the intersecting line.
Angle 5 is above line m and to the left of the intersecting line.
Angle 6 is above line m and to the right of the intersecting line.
Angle 7 is below line m and to the left of the intersecting line.
Angle 8 is below line m and to the right of the intersecting line.
(1 point)
Responses
The measure of angle 2 plus the measure of angle 4 equals 180 degrees.
Image with alt text: The measure of angle 2 plus the measure of angle 4 equals 180 degrees.
The measure of angle 1 equals the measure of angle 8.
Image with alt text: The measure of angle 1 equals the measure of angle 8.
The measure of angle 6 plus the measure of angle 3 equals 180 degrees.
Image with alt text: The measure of angle 6 plus the measure of angle 3 equals 180 degrees.
The measure of angle 7 equals the measure of angle 6.
The measure of angle 7 equals the measure of angle 6.
To prove that lines l and m are parallel, the following fact would allow us to do so:
The measure of angle 2 plus the measure of angle 4 equals 180 degrees.
This is because when a transversal intersects two parallel lines, the corresponding angles formed by the transversal and the lines are congruent. If the measures of angle 2 and angle 4 add up to 180 degrees, it means that they are supplementary angles. Since supplementary angles are a pair of angles that add up to 180 degrees, it suggests that lines l and m are indeed parallel.