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.
Image with alt text: The measure of angle 7 equals the measure of angle 6.
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The fact that would allow you to prove that lines l and m are parallel is: The measure of angle 2 plus the measure of angle 4 equals 180 degrees. This is because if the alternate interior angles formed by the transversal (angles 2 and 4) are congruent, then the lines are parallel.
To prove that lines l and m are parallel, we need to use the fact that corresponding angles formed by a transversal are congruent. In this case, we have:
Angle 2 and Angle 6 are corresponding angles formed by the transversal intersecting line l and line m. If the measure of angle 2 plus the measure of angle 6 equals 180 degrees, then we can conclude that lines l and m are parallel.
Therefore, the fact that would allow us to prove that lines l and m are parallel is:
"The measure of angle 2 plus the measure of angle 6 equals 180 degrees."