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Properties of Parallel Lines Calculator

Parallel-line test. Choose an angle relationship to decide whether two lines are parallel, with the reason—for parallel theorems.

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Equal corresponding/alternate or supplementary co-interior ⇒ parallel
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Choose the angle relationship given in the problem

📖 Tutorial | Testing for Parallel Lines

1. Definition
If a transversal gives equal corresponding, equal alternate, or supplementary co-interior angles, the lines are parallel.
2. Formula & Notation
PropertyParallel → angle relations
TestAngle relations → parallel
3. Properties & Laws
  • Equal corresponding ⇒ parallel;
  • Equal alternate ⇒ parallel;
  • Supplementary co-interior ⇒ parallel;
  • Property and test are converses.
4. Steps
  1. Choose the given angle relationship;
  2. Click "Decide";
  3. Read the conclusion and reason.
5. Worked Examples
Example: alternate angles are equal.
Solution: the lines are parallel, by equal alternate angles.
6. Common Pitfalls
Equal co-interior angles do not prove it (unless both 90°);
Property and test point opposite ways;
Need a common transversal.

❓ FAQ | Parallel Lines Test

What tests prove parallel lines?
Equal corresponding or alternate, or supplementary co-interior.
Property vs test?
Property: parallel→angles; test: angles→parallel.
Do equal co-interior prove it?
No, unless both are 90°.
Two lines parallel to the same line?
Parallel to each other (transitivity).
When alternate angles equal?
The lines are parallel.
Corresponding not equal means?
The lines are definitely not parallel.