6. Which of the following facts, if true, would allow you to prove that line l and m are parallel?
A.angle m + angle 4= 180
B. angle 1 = angle 8 **
C. angle 6+angle 3 = 180
D. angle 7= angle 6
something is missing here.
I cant figure out how to include the pic of it
just describe the picture, mentioning the lines and angles. For example
Given lines l (AB) and m (CD), a transversal crosses them, intersecting
line l at P
line m at Q
angle 1 is APQ
etc.
Then we can reproduce your diagram.
To determine if line l and m are parallel, you can use the properties of parallel lines and transversals.
In this case, if angle 1 is congruent (equal) to angle 8, then it would prove that line l and m are parallel. Therefore, option B is the correct choice.
To understand why angle 1 being equal to angle 8 proves the parallelism of line l and m, you can use the following explanation:
When a transversal (such as line l) intersects two parallel lines (such as line m), several pairs of angles are formed. These pairs of angles have specific relationships based on the properties of parallel lines:
- Corresponding Angles: When a transversal intersects two parallel lines, the angles located at the same position on each line are called corresponding angles. Corresponding angles are congruent (equal) to each other.
- Alternate Interior Angles: When a transversal intersects two parallel lines, the angles located between the two lines and on opposite sides of the transversal are called alternate interior angles. Alternate interior angles are congruent (equal) to each other.
- Alternate Exterior Angles: When a transversal intersects two parallel lines, the angles located outside the two lines and on opposite sides of the transversal are called alternate exterior angles. Alternate exterior angles are congruent (equal) to each other.
In this case, angle 1 and angle 8 are corresponding angles because they are located at the same position on line l and line m. Therefore, if angle 1 is congruent (equal) to angle 8, we can conclude that line l and m are parallel.