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Answer :
Corresponding angles: If two lines are cut by a transversal, and the corresponding angles are congruent, then the lines are parallel.
- 1. Draw two lines, and then draw a transversal that intersects them.
- 2. Identify the corresponding angles. Corresponding angles are two angles that are on the same side of the transversal, and they are in corresponding positions relative to the two lines.
- 3. Measure the corresponding angles. If the corresponding angles are congruent, then the lines are parallel.
For example, in the diagram below, lines `l` and `m` are parallel. Angle `1` is corresponding to angle `5`, angle `2` is corresponding to angle `6`, and angle `3` is corresponding to angle `4`. Since angles `1` and `5`, `2` and `6`, and `3` and `4` are all congruent, then lines `l` and `m` are parallel.
[Diagram of two lines, `l` and `m`, cut by a transversal. Angles 1, 2, 3, 4, 5, and 6 are labeled.]
The converse of the corresponding angles theorem also holds. This means that if two lines are cut by a transversal, and the corresponding angles are not congruent, then the lines are not parallel.
Here are some other ways to prove that lines are parallel when cut by a transversal:
- Alternate interior angles: If two lines are cut by a transversal, and the alternate interior angles are congruent, then the lines are parallel.
- Same-side interior angles: If two lines are cut by a transversal, and the same-side interior angles are supplementary, then the lines are parallel.
- These are just a few of the ways to prove that lines are parallel when cut by a transversal. The specific method that you use will depend on the specific problem that you are trying to solve.
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