Alternate Interior Angles Theorem

Alternate Interior Angles Theorem. The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent. Consider the given figure, EF and GH are the two parallel lines.

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We know that, if a transversal intersects any two parallel lines, the corresponding angles and vertically opposite. The term alternate interior angles is often used when two lines are cut by a third line, a transversal. Statement: The theorem states that if a transversal intersects parallel lines, the alternate interior angles are congruent.

Hence, both the angles are equal.

If two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent, according to the Alternate Interior Angles Theorem.

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When a transversal crosses two other lines, it creates an exterior and interior for the parallel lines. So let's do exactly what we did when we proved the Alternate Interior Angles Theorem, but in reverse - going from congruent alternate angles to showing congruent corresponding angles. Learn vocabulary, terms, and more with flashcards, games, and other study tools.