copies using any of the three procedures – Discussion Forum

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Piyush365

Asked: October 5, 2026In: Class 9 Maths

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.

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 ...