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How Prove Two Lines Are Parallel?

Maya Lin-Takahashi • • 4 min read
How Prove Two 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

interior angles
The measure of the exterior angle at a vertex is unaffected by which side is extended: the two exterior angles that can be formed at a vertex by extending alternately one side or the other are vertical angles and thus are equal.
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are supplementary, then the lines are parallel. If two lines are parallel to the same line, then they are parallel to each other.

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 prove two lines are parallel without angles?

If two lines have a transversal which forms alternative interior angles that are congruent, then the two lines are parallel. If two lines have a transversal which forms corresponding angles that are congruent, then the two lines are parallel.

Maya Lin-Takahashi
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Maya Lin-Takahashi

Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.