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Piyush365
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Asked: 2026-10-05T09:33:51+00:00 In:

Let us see a third method to tile the plane using a 4-gon. Focus on only two coloured copies of SOME sharing a vertex. What do you see? It appears that each 4-gon is just a shifted copy of the other. Let us see exactly how. Draw two copies of SOME as shown in Fig. 12.42 so that the diagonals EO and E’O’ are collinear with O = E’. Now place a cutout of one copy on top of SOME with diagonal EO drawn on it. Slide this cutout so that segment EO moves along EO’ until EO matches E’O’. Verify that your cutout exactly matches S’O’M’E’. (i) Prove the exact match of SOME with S’O’M’E’ using four parallelograms. (ii) Follow the described procedure along each diagonal of the starting coloured 4-gon in both directions to get 4 new 4-gons. Using these 4 copies, repeat the procedure 4 more times to place 4 new copies, resulting in a 3 by 3 grid of 9 copies exactly like the 9 coloured copies in Fig. 12.42. These 9 copies meet each other only at vertices and once again the blank spaces among them also form 4-gons congruent to SOME!

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(i) The displacement vector mapping E to O (E’) defines four parallelograms: E E’ S’ S, E E’ O’ O and E E’ M’ M. Translations preserve edge lengths and angles, guaranteeing an exact congruent match. (ii) Translating along both diagonal directions generates a doubly periodic lattice where remaining gaps naturally form congruent inverted quadrilaterals.

Class 9 Ganita Manjari part 2 Chapter 12 Solutions
Class 9 Ganita Manjari Part 2 Chapter 12 Page 80 Question Answer

cbse released class 9 ganita manjari part 2 bookchapter 12 quadrilaterals (ganita manjari 2) solutionsfollow the described procedure along each diagonal ofganita manjari part 2 solutions available!prove the exact match of somethird method to tile the plane using a 4-gon
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    1. (i) Translating the quadrilateral by the vector EO shifts each vertex by the same distance and direction. This translation creates four parallelograms connecting original vertices to shifted counterparts: E E’ O’ O, E E’ S’ S and E E’ M’ M. Because translation is a rigid motion preserving all side lengths and angles, S’O’M’E’ is identically congruent to SOME. (ii) Repeating this translation along both diagonal directions forms a regular grid of nine quadrilaterals touching at vertices, leaving interior voids that perfectly fit inverted copies of SOME.

       

      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/

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