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If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:
- a)Equal
- b)Sum of the two angles is 360°
- c)Complementary
- d)Supplementary
Correct answer is option 'A'. Can you explain this answer?
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Understanding Alternate Interior Angles
When two parallel lines are intersected by a transversal, certain angle relationships are formed. One significant relationship is that of the alternate interior angles.
Definition of Alternate Interior Angles
- Alternate interior angles are pairs of angles that are located between the two parallel lines, but on opposite sides of the transversal.
Properties of Parallel Lines and Transversals
- When two lines are parallel, the angles formed by a transversal have specific relationships:
- Corresponding angles are equal.
- Same-side interior angles are supplementary (sum to 180 degrees).
- Alternate interior angles are equal.
Why Alternate Interior Angles are Equal
- The concept relies on the definition of parallel lines:
- Parallel lines never meet and maintain a constant distance apart.
- The transversal creates a symmetrical angle formation.
- Since the alternate interior angles are formed by two lines that are parallel, they must be equal due to the nature of parallel lines and the rules of Euclidean geometry.
Conclusion
- Therefore, when two parallel lines are intersected by a transversal, the pair of alternate interior angles are indeed equal. This confirms that the correct answer to the question is option 'A'.
Understanding these relationships is crucial in geometry and helps in solving various problems involving angles formed by parallel lines and transversals.
When two parallel lines are intersected by a transversal, certain angle relationships are formed. One significant relationship is that of the alternate interior angles.
Definition of Alternate Interior Angles
- Alternate interior angles are pairs of angles that are located between the two parallel lines, but on opposite sides of the transversal.
Properties of Parallel Lines and Transversals
- When two lines are parallel, the angles formed by a transversal have specific relationships:
- Corresponding angles are equal.
- Same-side interior angles are supplementary (sum to 180 degrees).
- Alternate interior angles are equal.
Why Alternate Interior Angles are Equal
- The concept relies on the definition of parallel lines:
- Parallel lines never meet and maintain a constant distance apart.
- The transversal creates a symmetrical angle formation.
- Since the alternate interior angles are formed by two lines that are parallel, they must be equal due to the nature of parallel lines and the rules of Euclidean geometry.
Conclusion
- Therefore, when two parallel lines are intersected by a transversal, the pair of alternate interior angles are indeed equal. This confirms that the correct answer to the question is option 'A'.
Understanding these relationships is crucial in geometry and helps in solving various problems involving angles formed by parallel lines and transversals.
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If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:a)Equalb)Sum of the two angles is 360°c)Complementaryd)SupplementaryCorrect answer is option 'A'. Can you explain this answer?
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If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:a)Equalb)Sum of the two angles is 360°c)Complementaryd)SupplementaryCorrect answer is option 'A'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:a)Equalb)Sum of the two angles is 360°c)Complementaryd)SupplementaryCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two parallel lines are intersected by a transversal then, pair of alternate interior angles are:a)Equalb)Sum of the two angles is 360°c)Complementaryd)SupplementaryCorrect answer is option 'A'. Can you explain this answer?.
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