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Piyush365
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Asked: 2026-10-05T09:34:20+00:00 In:

Validity of tiling methods. Show using reasoning that each of the three tiling methods we saw produces a tiling of the plane using the given 4-gon. You have to prove that when we place new copies using any of the three procedures, the entire plane is covered with no gaps and no overlaps. First, think carefully about what it means to prove this. Then find a proof for each procedure.

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Method 1: 180° edge rotations place all four interior angles around each shared vertex, summing to 360° without gaps or overlaps. Methods 2 and 3: Parallelograms tile the plane, so positioning copies preserves edge congruences and seamlessly tiles the entire plane.

Class 9 Chapter 12 Quadrilaterals solutions
Class 9 maths Ganita Manjari Part 2 book and Solutions

cbse released class 9 ganita manjari part 2 bookchapter 12 quadrilaterals (ganita manjari 2) solutionscopies using any of the three proceduresfind a proof for each procedureganita manjari part 2 solutions available!using reasoning that each of the three tiling
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    1. A valid tiling requires edge lengths to match identically and all interior angles meeting at every vertex to sum to 360° without gaps or overlaps.

      • Method 1: Half-turn rotations around edge midpoints bring each of the four angles of the 4-gon together at every vertex, summing to 360° with matching adjacent edges.
      • Methods 2 & 3: Inscribing the 4-gon into a Varignon parallelogram grid or translating along diagonals uses periodic parallelogram tilings, naturally filling intervening spaces with congruent copies.

       

      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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