Readers ask: Which Construction Of Parallel Lines Is Justified By The Theorem?

Which construction of parallel lines is justified by the theorem when two lines are intersected?

When two lines are intersected by a transversal and alternate interior angles are congruent, the lines are parallel. When two lines are intersected by a transversal and the corresponding angles are congruent, the lines are parallel. 3 The diagram below shows the construction of through point P parallel to.

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.

What theorem proves that two lines are parallel?

If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

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Which property of parallel lines is used in construction of parallel lines?

This construction works by using the fact that a transverse line drawn across two parallel lines creates pairs of equal corresponding angles. It uses this in reverse – by creating two equal corresponding angles, it can create the parallel lines.

When two lines are intersected by a transversal and the corresponding angles are congruent?

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

When two lines are intersected by a transversal and the corresponding angles are congruent the lines are parallel?

If two parallel lines are cut by a transversal, the corresponding angles are congruent. If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel. Interior Angles on the Same Side of the Transversal: The name is a description of the “location” of the these angles.

What are five ways to prove 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.

How do you know if lines are parallel?

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.

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What must be true for lines A and B to be parallel lines?

Lines a and b are parallel because their corresponding angles are congruent. m∠2 = (3x – 3)°. Lines e and f are parallel because their alternate exterior angles are congruent.

What do parallel lines give you?

When you have two parallel lines cut by a transversal, you get four acute angles and four obtuse angles (except when you get eight right angles). All the acute angles are congruent, all the obtuse angles are congruent, and each acute angle is supplementary to each obtuse angle.

How do you make parallel lines?

How to Construct Two Parallel Lines

  1. The first thing you do is draw a straight line. It can be any length.
  2. Step 2: Steps Two & Three. Place the stylus of the compass on the point, and swing the compass down to make two marks on the line.
  3. Step 3: Step Four & Five.
  4. Connect these 3 points, and now you have 2 parallel lines!

What is transversal theorem?

If two lines are intersected by a transversal, then alternate interior angles, alternate exterior angles, and corresponding angles are congruent. 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.

What are the three 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.
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What are the types of parallel lines?

Properties of parallel line

  • Two lines cut by a transversal line are parallel when the corresponding angles are equal.
  • Two lines cut by a transversal line are parallel when the alternate interior angles are equal.
  • Two lines cut by a transversal line are parallel when the alternate exterior angles are equal.

Can 2 rays be parallel?

Parallel rays two rays are parallel if the corresponding lines determined by them are parallel. In other words two rays in the same plane are parallel if they do not intersect each other even if extended indefinitely beyond their initial points.

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