# What is the theorem for parallel lines?

## What is the theorem for parallel lines?

Alternate Interior Angle Theorem The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .

Are parallel lines in a triangle congruent?

2. If there are corresponding angles between parallel lines, they are congruent. 3. If there are congruent triangles, all their angles are congruent.

### What are the 5 ways to prove that 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.

Why are parallel lines congruent?

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . When the lines are parallel, the corresponding angles are congruent . If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .

#### What are congruent lines?

If two line segments are congruent, that means that they are of equal lengths. If two shapes are congruent that means that if you pick one up and put it on the other, they will coincide throughout (they will match up perfectly and you will not be able to see the one on the bottom).

How do you prove 2 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.

## Are parallel lines equal?

Parallel lines are equidistant lines (lines having equal distance from each other) that will never meet. These are some examples of parallel lines in different directions: horizontally, diagonally, and vertically. Another important fact about parallel lines: they share the same direction.

How do you know if angles are parallel?

Two angles are corresponding if they are in matching positions in both intersections. If you check only a single pair of corresponding angles and they are equal, then the two lines are parallel.

### What happens when 2 lines are parallel?

Two lines are parallel if they have the same slope, or if they are vertical. If two parallel lines form a system, there are no solutions to the system. If lines intersect, the lines cross in one point. The angles at which the two lines intersect can vary.

What is the difference between parallel and congruent?

Parallel, means running along each other. It is used mostly for straight lines, but two curved lines can also be ‘parallel’, like for example the rails of the railway. Congruent means equal in both shape and size.

#### What are the rules of parallel lines?

Parallel Lines. Lines are parallel if they are always the same distance apart (called “equidistant”), and will never meet. Just remember: Always the same distance apart and never touching. The red line is parallel to the blue line in each of these examples: Parallel lines also point in the same direction.

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.

## What is true of parallel lines?

Line art drawing of parallel lines and curves. In geometry, parallel lines are lines in a plane which do not meet; that is, two straight lines in a plane that do not intersect at any point are said to be parallel. Colloquially, curves that do not touch each other or intersect and keep a fixed minimum distance are said to be parallel.