How do you prove lines are parallel proof?

If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.

What converse proves the lines are parallel?

The converse of the theorem is true as well. If two corresponding angles are congruent, then the two lines cut by the transversal must be parallel. Similarly, if two alternate interior or alternate exterior angles are congruent, the lines are parallel.

Is it possible to prove that lines P and Q are parallel if so explain how?

Z1 = 12 1. is it possible to prove that lines p and q are parallel? If the lines are cut by a transversal so that (alternate interior, alternate exterior, corresponding) angles are congruent, then the lines are parallel.

What are the 5 ways to prove that 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.

What are properties of parallel lines?

Properties Of Parallel Lines

The corresponding angles are equal.
The vertically opposite angles are equal.
The alternate interior angles are equal.
The alternate exterior angles are equal.
The pair of interior angles on the same side of the transversal is supplementary.

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

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.

Can you prove a statement using its converse?

Going from a statement to its converse is the fallacy of affirming the consequent. However, if the statement S and its converse are equivalent (i.e., P is true if and only if Q is also true), then affirming the consequent will be valid.

Which theorem guarantees lines are parallel?

Theorem 21: If two lines and a transversal form consecutive interior angles that are supplementary, then the lines are parallel.

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

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 are four ways that could be used to prove that two lines are parallel?

Ways to Prove Two Lines Parallel

Show that corresponding angles are equal.
Show that alternative interior angles are equal.
Show that consecutive interior angles are supplementary.
Show that consecutive exterior angles are supplementary.
In a plane, show that the lines are perpendicular to the same line.

What is a parallel lines in math?

CCSS.Math: 4.G.A.1. Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

What is the rule for parallel lines?

The rule for parallel lines is that the lines should not meet each other. In other words, if two straight lines in the same plane are the same distance apart and they never meet each other, they are called parallel lines.

How do you prove that lines are parallel?

Proving Lines are Parallel. Students learn the converse of the parallel line postulate. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

Are perpendicular lines intersecting lines?

Perpendicular lines are intersecting lines that are at right angles to each-other. For lines in the x-y plane, every vertical (x = constant) line is perpendicular to every horizontal (y = constant) line.

How are perpendicular lines different to intersecting lines?

Perpendicular lines and intersecting lines are the same because they both describe 2 lines that cross one another… They are different because perpendicular lines cross one another in a specific way. The intersection of perpendicular lines forms 90 degree angles, while intersecting lines just describes 2 lines crossing.

What are parallel lines and angles?

Angles in parallel lines. Parallel lines are lines which are always the same distance apart and never meet. Arrowheads show lines are parallel. When a pair of parallel lines is cut with another line known as an intersecting transversal, it creates pairs of angles with special properties. Corresponding angles are equal. The lines make an F shape.