Taking into account the definition of corresponding angles and Corresponding Angles Theorem, if the corresponding angles are congruent, then two lines cut it by a transversal are parallel.
First of all, remember that a transverse line is a line that crosses or passes through two other lines. Sometimes the other two lines are parallel and the transversal passes through both lines at the same angle. However, the other two lines do not have to be parallel for a transversal to cross them.
Corresponding angles are angles formed when a transverse line crosses two straight lines. These angles are formed at equivalent corners or at corners corresponding to the transversal when two lines are intersected by a third line.
In other words, if a transversal line intersects two parallel lines, the corresponding angles are those that are on the same side of the parallels and on the same side of the transversal.
- Corresponding Angles Theorem
The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal, then the corresponding pairs of angles are congruent.
Remember that if two angles are congruent, then they have the same measure.
The opposite of this theorem is also true: If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.
In summary, if the corresponding angles are congruent, then two lines cut it by a transversal are parallel.
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