# What are the theorems used in proving parallel lines cut by a transversal?

Space and Astronomy**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.

Contents:

## What theorem is parallel lines cut by a transversal?

If two parallel lines are cut by a transversal, then, **Alternate Exterior Angles are congruent**. If two parallel lines are cut by a transversal, then corresponding angles are congruent.

## What are the theorems for parallel lines?

**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.

## What are the four theorems that will prove that the lines are parallel?

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 is the transversal theorem?

The perpendicular transversal theorem states that **if two parallel lines are in a plane, a line perpendicular to one line will be perpendicular to the other**.

## What are properties of parallel lines?

Properties of Parallel Lines

**Corresponding angles are equal**. Vertical angles/ Vertically opposite angles are equal. Alternate interior angles are equal. Alternate exterior angles are equal.

## How do you do parallel lines and Transversals?

Video quote: *These two parallel lines when a transversal crosses two lines you get one two three four angles there and then one two three four more angles here.*

## What is the property of transversal?

Properties of Transversal

**Vertically opposite angles are equal**. Corresponding angles are equal. The interior angles formed on the same side of the transversal are supplementary. Alternate angles are equal.

## What is parallel lines write all the properties of parallel lines and a transversal?

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

## What is the condition for parallel lines Class 10?

Parallel lines **have the same slope and will never intersect**. Example : Lines 3x+4y=1 and 3x+4y=5 are parallel.

## What conditions are required for two lines intersected by a transversal to be parallel?

First, if a transversal intersects two lines so that **corresponding angles are congruent**, then the lines are parallel. Second, if a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.

## When two parallel lines are intersected by a transversal which pair of angles are always supplementary?

consecutive interior angles

If two parallel lines are cut by a transversal, then the pairs of **consecutive interior angles** formed are supplementary . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .

## When two parallel lines are intersected by a transversal angles are formed in each pair of corresponding angles are?

When two parallel lines are intersected by a transversal, then corresponding angles are **always equal**.

## When two parallel lines are intersected by a transversal how many angles are formed?

eight angles

When a transversal intersects with two parallel lines **eight angles** are produced. The eight angles will together form four pairs of corresponding angles.

## When two parallel lines are intersected by a transversal angles are formed four two eight six?

Answer. Step-by-step explanation: When a transversal intersects with two parallel lines eight angles are produced. **The eight angles will together form four pairs of corresponding angles**.

## What happens when two parallel lines are intersected by a transversal?

When two parallel lines are intersected by the transversal, **eight angles are formed**. The eight angles include corresponding angles, alternate interior and exterior angles, vertically opposite angles, and co-interior angles.

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