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Converse of Alternate Angles Theorem

If alternate ...

Question

If alternate interior angles are equal, transversal intersects parallel lines.

A

True

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B

False

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Solution

The correct option is A True

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If two parallel lines are intersected by a transversal, then alternate interior angles are equal.

Q. If a transversal intersects two lines such that a pair of alternate interior angles is equal , then the two lines are parallel.

Q. The alternate interior angles are congruent when the transversal intersects two parallel lines.

Q. Read the following statements which are taken as axioms :
(i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal.
(ii) If a transversal intersect two parallel lines, then alternate interior angles are equal.
Is this system of axioms consistent?

Q. Alternate interior angles are angles formed when two parallel or non-parallel lines are intersected by a transversal.

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