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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 ...
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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.
- 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 .?.
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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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 .?, a detailed solution 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 .? has been provided alongside types of 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 .? theory, EduRev gives you an
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