(i) By the Midpoint Theorem, each segment connecting two midpoints equals half the opposite third side and is parallel to it. Therefore, PQ = RC = BR, QR = AP = PB and RP = AQ = QC. By SSS congruence, △PQR ≅ △QPA ≅ △RPB ≅ △CQR. (ii) Yes. Through points P, Q and R, draw lines parallel to QR, PR and PRead more
(i) By the Midpoint Theorem, each segment connecting two midpoints equals half the opposite third side and is parallel to it. Therefore, PQ = RC = BR, QR = AP = PB and RP = AQ = QC. By SSS congruence, △PQR ≅ △QPA ≅ △RPB ≅ △CQR.
(ii) Yes. Through points P, Q and R, draw lines parallel to QR, PR and PQ respectively. Their intersections form the vertices C, B and A of △ABC.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)
The proposition is true because every square contains four 90-degree angles. However, the converse ("If all angles of a quadrilateral are equal, then it is a square") is false. A rectangle serves as an exact counterexample: all four of its interior angles are equal to 90 degrees, but its adjacent siRead more
The proposition is true because every square contains four 90-degree angles. However, the converse (“If all angles of a quadrilateral are equal, then it is a square”) is false. A rectangle serves as an exact counterexample: all four of its interior angles are equal to 90 degrees, but its adjacent sides are unequal, making it a non-square.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
Both the proposition and its converse ("If corresponding angles formed by a transversal with two lines are equal, then the lines are parallel") are true. The proposition follows directly from the parallel lines property, while the converse is established by the corresponding angles axiom, which veriRead more
Both the proposition and its converse (“If corresponding angles formed by a transversal with two lines are equal, then the lines are parallel”) are true. The proposition follows directly from the parallel lines property, while the converse is established by the corresponding angles axiom, which verifies that two lines cut by a transversal are indeed parallel.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
Both the proposition and its converse ("If IE = IF, then AB = AC") are true. When AB = AC, the triangle is isosceles, creating congruent sub-triangles and symmetry that guarantees IE = IF. Conversely, if the extended bisector segments satisfy IE = IF, geometric congruence of the resulting inner segmRead more
Both the proposition and its converse (“If IE = IF, then AB = AC”) are true. When AB = AC, the triangle is isosceles, creating congruent sub-triangles and symmetry that guarantees IE = IF. Conversely, if the extended bisector segments satisfy IE = IF, geometric congruence of the resulting inner segments forces the base angles to be equal, ensuring AB = AC.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
The proposition and its converse ("If a + x = a + y, then x = y") are both true. The proposition follows from the addition property of equality. The converse holds by the cancellation law: subtracting the real number a from both sides of a + x = a + y yields x = y, making algebraic equation steps fuRead more
The proposition and its converse (“If a + x = a + y, then x = y”) are both true. The proposition follows from the addition property of equality. The converse holds by the cancellation law: subtracting the real number a from both sides of a + x = a + y yields x = y, making algebraic equation steps fully reversible.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
(i) If P, Q, R are the midpoints of sides AB, AC, BC respectively of △ABC, show that △PQR is congruent to △QPA and to two other triangles which you should identify. (ii) Suppose someone erases △ABC, leaving only △PQR on the paper. Can you reconstruct △ABC from △PQR?
(i) By the Midpoint Theorem, each segment connecting two midpoints equals half the opposite third side and is parallel to it. Therefore, PQ = RC = BR, QR = AP = PB and RP = AQ = QC. By SSS congruence, △PQR ≅ △QPA ≅ △RPB ≅ △CQR. (ii) Yes. Through points P, Q and R, draw lines parallel to QR, PR and PRead more
(i) By the Midpoint Theorem, each segment connecting two midpoints equals half the opposite third side and is parallel to it. Therefore, PQ = RC = BR, QR = AP = PB and RP = AQ = QC. By SSS congruence, △PQR ≅ △QPA ≅ △RPB ≅ △CQR.
(ii) Yes. Through points P, Q and R, draw lines parallel to QR, PR and PQ respectively. Their intersections form the vertices C, B and A of △ABC.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-12/
See lessIf a quadrilateral is a square, then all its angles are equal.
The proposition is true because every square contains four 90-degree angles. However, the converse ("If all angles of a quadrilateral are equal, then it is a square") is false. A rectangle serves as an exact counterexample: all four of its interior angles are equal to 90 degrees, but its adjacent siRead more
The proposition is true because every square contains four 90-degree angles. However, the converse (“If all angles of a quadrilateral are equal, then it is a square”) is false. A rectangle serves as an exact counterexample: all four of its interior angles are equal to 90 degrees, but its adjacent sides are unequal, making it a non-square.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessIf two lines are parallel, then the corresponding angles formed by a transversal are equal.
Both the proposition and its converse ("If corresponding angles formed by a transversal with two lines are equal, then the lines are parallel") are true. The proposition follows directly from the parallel lines property, while the converse is established by the corresponding angles axiom, which veriRead more
Both the proposition and its converse (“If corresponding angles formed by a transversal with two lines are equal, then the lines are parallel”) are true. The proposition follows directly from the parallel lines property, while the converse is established by the corresponding angles axiom, which verifies that two lines cut by a transversal are indeed parallel.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessGiven any triangle ABC, let us bisect the angles at B and C. The bisectors meet at the incentre I of the triangle. Now extend the bisectors beyond I till they meet the opposite sides at E and F respectively, as shown. Proposition: If AB = AC, then IE = IF.
Both the proposition and its converse ("If IE = IF, then AB = AC") are true. When AB = AC, the triangle is isosceles, creating congruent sub-triangles and symmetry that guarantees IE = IF. Conversely, if the extended bisector segments satisfy IE = IF, geometric congruence of the resulting inner segmRead more
Both the proposition and its converse (“If IE = IF, then AB = AC”) are true. When AB = AC, the triangle is isosceles, creating congruent sub-triangles and symmetry that guarantees IE = IF. Conversely, if the extended bisector segments satisfy IE = IF, geometric congruence of the resulting inner segments forces the base angles to be equal, ensuring AB = AC.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessIf x = y, then a + x = a + y, where x, y and a are any three numbers. This proposition and its converse are routinely used while solving equations.
The proposition and its converse ("If a + x = a + y, then x = y") are both true. The proposition follows from the addition property of equality. The converse holds by the cancellation law: subtracting the real number a from both sides of a + x = a + y yields x = y, making algebraic equation steps fuRead more
The proposition and its converse (“If a + x = a + y, then x = y”) are both true. The proposition follows from the addition property of equality. The converse holds by the cancellation law: subtracting the real number a from both sides of a + x = a + y yields x = y, making algebraic equation steps fully reversible.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See less