Which theorem best justifies why Lines J and K must be parallel?

The converse alternate exterior angles theorem justifies why lines j and k must be parallel. The converse alternate exterior angles theorem states that if two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

Similarly, it is asked, which lines are parallel justify your answer?

If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Subsequently, question is, which lines must be parallel? because they are on the interior of lines L and K and on the same side of the transversal M therefore lines L and K must be parallel. because if two lines are cut by a transversal. and same side interior angles are supplementary then the lines are parallel.

Beside this, which theorem correctly justifies why the lines m and n are parallel when cut by transversal k?

the alternate interior angles theorem

How do you justify parallel lines?

The first is if the corresponding angles, the angles that are on the same corner at each intersection, are equal, then the lines are parallel. The second is if the alternate interior angles, the angles that are on opposite sides of the transversal and inside the parallel lines, are equal, then the lines are parallel.

What are five ways to prove two lines are parallel?

Terms in this set (6)

#1. if corresponding angles are congruent.
#2. if alternate interior angles are congruent.
#3. if consecutive, or same side, interior angles are supplementary.
#4. if two lines are parallel to the same line.
#5. if two lines are perpendicular to the same line.
#6. if alternate exterior angles are congruent.

Which lines are parallel justify your answer lines P and Q?

Lines p and q are parallel because same side interior angles are congruent. Lines p and q are parallel because alternate exterior angles are congruent Lines l and m are parallel because same side interior angles are supplementary Lines l and m are parallel because alternate interior angles are supplementary.

What theorem proves that two lines are parallel?

If two lines are cut by a transversal and the alternate exterior angles are equal, then the two lines are parallel. Angles can be equal or congruent; you can replace the word "equal" in both theorems with "congruent" without affecting the theorem. So if ∠B and ∠L are equal (or congruent), the lines are parallel.

Can you prove that lines P and Q are parallel?

is it possible to prove that lines p and q are parallel? If so, state the postulate or theorem you would use. If the lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding) angles are congruent, then the lines are parallel.

How do you prove two lines are parallel on a graph?

Two lines are parallel if they have the same slope, or if they are both vertical. Try this Drag any of the 4 points below to move the lines. Note they are parallel when the slopes are the same. When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line.

Which theorem correctly justifies?

alternate interior angles theorem

How do you prove that two lines are parallel in an equation?

We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.

Are parallel lines equal?

are equal in measure. If two parallel lines are cut by a transversal, the alternate exterior angles are congruent. If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel.

What is an example of parallel lines?

For example, squares, rectangles, and parallelograms have sides across from each other that are parallel. Each line has many parallels. Any line that has the same slope as the original will never intersect with it. Lines that would never cross, even if extended forever, are parallel.

How do you prove two lines are parallel without angles?

If two lines have a transversal which forms alternative interior angles that are congruent, then the two lines are parallel. If two lines have a transversal which forms corresponding angles that are congruent, then the two lines are parallel.