Without Step 5, any carry generated by the leftmost column is discarded, resulting in an incorrect answer. The algorithm still works correctly when no final carry is produced, such as 1234 + 2345 = 3579. However, it fails when the leading digits sum to ten or more; for example, 5000 + 6000 yields 10Read more
Without Step 5, any carry generated by the leftmost column is discarded, resulting in an incorrect answer. The algorithm still works correctly when no final carry is produced, such as 1234 + 2345 = 3579. However, it fails when the leading digits sum to ten or more; for example, 5000 + 6000 yields 1000 instead of 11000 because the final carry is ignored.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 11 The World of Algorithms Question Answer (2026-27)
In quadrilateral ABCD, sides sharing an endpoint with AB are DA and BC, whereas side CD is opposite to AB. The angles sharing a side with ∠A are ∠B and ∠D and the non-adjacent angle is ∠C. Generally, opposite sides are two sides with no common vertex and opposite angles are two internal angles whoseRead more
In quadrilateral ABCD, sides sharing an endpoint with AB are DA and BC, whereas side CD is opposite to AB. The angles sharing a side with ∠A are ∠B and ∠D and the non-adjacent angle is ∠C. Generally, opposite sides are two sides with no common vertex and opposite angles are two internal angles whose vertices share no common edge.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)
Let V be a vertex where adjacent sides form rays VA and VB, with V' being the opposite vertex. The rays divide the plane into two angular regions. The internal angle at V is defined as the region between rays VA and VB containing the segment VV' near V. For a convex vertex, this measures under 180°,Read more
Let V be a vertex where adjacent sides form rays VA and VB, with V’ being the opposite vertex. The rays divide the plane into two angular regions. The internal angle at V is defined as the region between rays VA and VB containing the segment VV’ near V. For a convex vertex, this measures under 180°, while for a reflex vertex, it exceeds 180°.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)
When AB ∥ DC, consecutive interior angles along transversals add up to 180°, so every internal angle is strictly less than 180°, making it strictly convex. However, if we only assume AB = CD or ∠A = ∠C, ABCD can be non-convex. An example is a symmetric arrowhead dart, where opposite side lengths orRead more
When AB ∥ DC, consecutive interior angles along transversals add up to 180°, so every internal angle is strictly less than 180°, making it strictly convex. However, if we only assume AB = CD or ∠A = ∠C, ABCD can be non-convex. An example is a symmetric arrowhead dart, where opposite side lengths or opposite base angles match while one vertex indents inward beyond 180°.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)
The three lines create seven separate regions. Placing point D inside the central triangle forms a non-convex quadrilateral with an inward dent. Placing D across side AC or in the corner region vertically opposite vertex B gives a convex quadrilateral whose diagonals intersect. For all other four ouRead more
The three lines create seven separate regions. Placing point D inside the central triangle forms a non-convex quadrilateral with an inward dent. Placing D across side AC or in the corner region vertically opposite vertex B gives a convex quadrilateral whose diagonals intersect. For all other four outer regions around sides AB and BC, edges cross each other, producing a self-intersecting quadrilateral.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 12 Quadrilaterals Question Answer (2026-27)
What happens if we do not include the fifth step in the algorithm above? Give examples where the algorithm will work correctly and where it will fail to work.
Without Step 5, any carry generated by the leftmost column is discarded, resulting in an incorrect answer. The algorithm still works correctly when no final carry is produced, such as 1234 + 2345 = 3579. However, it fails when the leading digits sum to ten or more; for example, 5000 + 6000 yields 10Read more
Without Step 5, any carry generated by the leftmost column is discarded, resulting in an incorrect answer. The algorithm still works correctly when no final carry is produced, such as 1234 + 2345 = 3579. However, it fails when the leading digits sum to ten or more; for example, 5000 + 6000 yields 1000 instead of 11000 because the final carry is ignored.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 11 The World of Algorithms Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-11/
See lessLet ABCD be a quadrilateral. (i) List all sides of ABCD adjacent to side AB. List all sides opposite to AB. (ii) List all angles of ABCD adjacent to ∠A. List all angles opposite to ∠A. (iii) Define a pair of opposite sides and a pair of opposite angles without using the names of the vertices.
In quadrilateral ABCD, sides sharing an endpoint with AB are DA and BC, whereas side CD is opposite to AB. The angles sharing a side with ∠A are ∠B and ∠D and the non-adjacent angle is ∠C. Generally, opposite sides are two sides with no common vertex and opposite angles are two internal angles whoseRead more
In quadrilateral ABCD, sides sharing an endpoint with AB are DA and BC, whereas side CD is opposite to AB. The angles sharing a side with ∠A are ∠B and ∠D and the non-adjacent angle is ∠C. Generally, opposite sides are two sides with no common vertex and opposite angles are two internal angles whose vertices share no common edge.
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 lessYou have used internal angles of quadrilaterals, but they too require an exact definition, just like how we gave one for a quadrilateral. Precisely define the internal angle of a quadrilateral at a given vertex. Your answer should work for a non-convex quadrilateral too. (Hint: use the opposite vertex as well.)
Let V be a vertex where adjacent sides form rays VA and VB, with V' being the opposite vertex. The rays divide the plane into two angular regions. The internal angle at V is defined as the region between rays VA and VB containing the segment VV' near V. For a convex vertex, this measures under 180°,Read more
Let V be a vertex where adjacent sides form rays VA and VB, with V’ being the opposite vertex. The rays divide the plane into two angular regions. The internal angle at V is defined as the region between rays VA and VB containing the segment VV’ near V. For a convex vertex, this measures under 180°, while for a reflex vertex, it exceeds 180°.
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 lessIn a quadrilateral ABCD, suppose AB ∥ DC. Can ABCD be non-convex? What if we instead assume AB = CD? What if we instead assume ∠A = ∠C?
When AB ∥ DC, consecutive interior angles along transversals add up to 180°, so every internal angle is strictly less than 180°, making it strictly convex. However, if we only assume AB = CD or ∠A = ∠C, ABCD can be non-convex. An example is a symmetric arrowhead dart, where opposite side lengths orRead more
When AB ∥ DC, consecutive interior angles along transversals add up to 180°, so every internal angle is strictly less than 180°, making it strictly convex. However, if we only assume AB = CD or ∠A = ∠C, ABCD can be non-convex. An example is a symmetric arrowhead dart, where opposite side lengths or opposite base angles match while one vertex indents inward beyond 180°.
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 lessConsider three non-collinear points A, B, C and draw the lines AB, BC, CA. For every possible location of point D in the plane outside these lines, decide if ABCD is self-intersecting, non-convex or convex. (Hint: the three lines divide the plane into 7 regions.)
The three lines create seven separate regions. Placing point D inside the central triangle forms a non-convex quadrilateral with an inward dent. Placing D across side AC or in the corner region vertically opposite vertex B gives a convex quadrilateral whose diagonals intersect. For all other four ouRead more
The three lines create seven separate regions. Placing point D inside the central triangle forms a non-convex quadrilateral with an inward dent. Placing D across side AC or in the corner region vertically opposite vertex B gives a convex quadrilateral whose diagonals intersect. For all other four outer regions around sides AB and BC, edges cross each other, producing a self-intersecting quadrilateral.
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 less