What Happens When Parallel Lines Are Intersected By A Transversal?

When the lines are parallel, the interior angles on the same side of the transversal are supplementary. If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.

When two parallel lines are intersected by a transversal which angles are formed?

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.

What parallel lines are cut by a transversal?

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.

How do you prove lines are parallel?

If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel. If two lines are cut by a transversal so the consecutive interior angles are supplementary, then the lines are parallel. If two lines are parallel to the same line, then they are parallel to each other.

Which situation shows 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 the angles between the two parallel lines?

the angle between parallel lines is undefined, or it can be either 0 or 180 degrees, or any multiple of 180 degrees.

What are the angles outside the two parallel lines?

Angles that are in the area between the parallel lines like angle H and C above are called interior angles whereas the angles that are on the outside of the two parallel lines like D and G are called exterior angles. Angles that are on the opposite sides of the transversal are called alternate angles e.g. H and B.

Which angles are equal in parallel lines?

Angles in parallel lines

  • 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. …
  • Alternate angles are equal. The lines make a Z shape which can also be back to front.

How do you prove two lines are supplementary?

Theorem 10.4: If two parallel lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary angles. Theorem 10.5: If two parallel lines are cut by a transversal, then the exterior angles on the same side of the transversal are supplementary angles.

Why are same side interior angles are always supplementary whenever lines are parallel?

The same-side interior angles theorem states that same-side interior angles are supplementary when the lines intersected by the transversal line are parallel. 2) Since the lines A and B are parallel, the same-side interior angles theorem states that same-side interior angles will be supplementary.

What are properties of parallel lines?

FAQs on Properties of Parallel Lines

  • The pairs of corresponding angles are equal.
  • The pairs of vertically opposite angles are equal.
  • The pairs of alternate interior angles are equal.
  • The pairs of alternate exterior angles are equal.

What are parallel lines examples?

Two or more lines that lie in the same plane and never intersect or meet each other are known as parallel lines. For example, let us assume two tall buildings in a neighborhood. They seem so tall and straight.

What angles are adjacent?

Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.

Which angles are congruent to ∠ 3?

Angles 1 and 3 are vertical angles. They are congruent. This can be written as ∠1 ≅ ∠3. If ∠1 measures 120° , then ∠3 measures 120°.

What are two parallel lines called?

In geometry, a transversal is a line that intersects two or more other (often parallel ) lines. In the figure below, line n is a transversal cutting lines l and m . When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .

What are the four angles formed between the two parallel lines?

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.

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.

What are the three examples of parallel lines?

In real life, while railroad tracks, the edges of sidewalks, and the markings on streets are all parallel, the tracks, sidewalks, and streets go up and down hills and around curves. Those three real-life examples are good, but not perfect, models of parallel lines. Consider railroad tracks.

What do parallel lines look like?

Lines that never intersect are parallel lines. Parallel lines do not form any angles. Parallel lines look like railroad tracks: they are always the same distance apart, running next to each other. … The lines do not intersect.

Do parallel lines have to be equal?

Lines are parallel if they are always the same distance apart (called “equidistant”), and will never meet.


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