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PQ and RS are two equal and parallel line segmaents . Any pojnt M not lyong on PQ and RS is joined to Q and S and line through p parallel to QM and through R parallel to SM meets at N . Prove that the line segments MN and PQ are equal and parallel to equal and parallel to each other. Plzz hep me .?
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PQ and RS are two equal and parallel line segmaents . Any pojnt M not ...
Given:
- PQ and RS are two equal and parallel line segments.
- M is a point not lying on PQ and RS.
- QM and SM are lines joining M to Q and S respectively.
- Line through P parallel to QM and line through R parallel to SM meet at N.

To prove:
- MN and PQ are equal and parallel to each other.

Proof:

1. Statement: PQ and RS are parallel line segments.
Reason: Given.

2. Statement: PQ and RS are equal line segments.
Reason: Given.

3. Statement: QM and SM are parallel lines.
Reason: By construction, QM and SM are lines joining the same point M to points Q and S respectively.

4. Statement: Line through P parallel to QM and line through R parallel to SM intersect at N.
Reason: Given.

5. Statement: ∠QMN = ∠RMP (corresponding angles)
Reason: Alternate interior angles formed by the transversal line PN and the parallel lines QM and PR.

6. Statement: ∠RMP = ∠PMN (corresponding angles)
Reason: Alternate interior angles formed by the transversal line NR and the parallel lines RM and PQ.

7. Statement: ∠QMN = ∠PMN
Reason: From statements 5 and 6, ∠QMN = ∠RMP = ∠PMN.

8. Statement: ∆QMN ≅ ∆PMN
Reason: From statement 7, ∠QMN = ∠PMN and MN is a common side.

9. Statement: MN = MN (common side)
Reason: Reflexive property of equality.

10. Statement: ∆QMN ≅ ∆PMN (ASA criterion)
Reason: From statements 8 and 9, ∆QMN ≅ ∆PMN by Angle-Side-Angle criterion.

11. Statement: MN = PQ (corresponding sides of congruent triangles)
Reason: By the congruence of ∆QMN and ∆PMN, their corresponding sides are equal.

12. Statement: MN || PQ (corresponding sides of congruent triangles)
Reason: By the congruence of ∆QMN and ∆PMN, their corresponding sides are parallel.

Therefore, we have proved that MN and PQ are equal and parallel to each other.
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PQ and RS are two equal and parallel line segmaents . Any pojnt M not lyong on PQ and RS is joined to Q and S and line through p parallel to QM and through R parallel to SM meets at N . Prove that the line segments MN and PQ are equal and parallel to equal and parallel to each other. Plzz hep me .?
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PQ and RS are two equal and parallel line segmaents . Any pojnt M not lyong on PQ and RS is joined to Q and S and line through p parallel to QM and through R parallel to SM meets at N . Prove that the line segments MN and PQ are equal and parallel to equal and parallel to each other. Plzz hep me .? 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 PQ and RS are two equal and parallel line segmaents . Any pojnt M not lyong on PQ and RS is joined to Q and S and line through p parallel to QM and through R parallel to SM meets at N . Prove that the line segments MN and PQ are equal and parallel to equal and parallel to each other. Plzz hep me .? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQ and RS are two equal and parallel line segmaents . Any pojnt M not lyong on PQ and RS is joined to Q and S and line through p parallel to QM and through R parallel to SM meets at N . Prove that the line segments MN and PQ are equal and parallel to equal and parallel to each other. Plzz hep me .?.
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