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If two parallel lines are cut by a trans...

If two parallel lines are cut by a transversal, then the alternate interior angles are equal

A

TRUE

B

FALSE

C

Cannot be determined

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To demonstrate that if two parallel lines are cut by a transversal, then the alternate interior angles are equal, we can follow these steps: ### Step-by-Step Solution: 1. **Draw Two Parallel Lines**: - Start by drawing two straight lines that are parallel to each other. Let's label them as line L and line M. 2. **Draw a Transversal**: - Next, draw a third line that intersects both parallel lines. This line will be called the transversal, and we can label it as line N. 3. **Identify Alternate Interior Angles**: - When the transversal intersects the parallel lines, it creates several angles. Identify two pairs of alternate interior angles. - For example, let’s label one pair as angle A and angle B, which are located on opposite sides of the transversal but inside the parallel lines. - Similarly, label another pair of alternate interior angles as angle C and angle D. 4. **State the Relationship**: - According to the properties of parallel lines cut by a transversal, we state that angle A is equal to angle B (∠A = ∠B) and angle C is equal to angle D (∠C = ∠D). 5. **Conclusion**: - Therefore, we conclude that if two parallel lines are cut by a transversal, then the alternate interior angles are equal.
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