find a pattern and guess the answers for n = 7 and n = 8 – Discussion Forum

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Piyush365

Asked: October 5, 2026In: Class 9 Maths

Counting diagonals of a polygon. (i) How should we define a diagonal of an n-gon? How many diagonals does an n-gon have? Make a table for small values of n. A 3-gon has no diagonals. A 4-gon has 2. How many diagonals does a 5-gon have? A 6-gon? Try to find a pattern and guess the answers for n = 7 and n = 8. Check your guesses by systematic counting. (ii) Can you guess a formula for the number of diagonals? How many diagonals get added when we increase the number of sides by 1? Can you now justify why the formula you guessed is true for all n?

(i) A diagonal connects two non-adjacent vertices. Diagonals: 3-gon: 0; 4-gon: 2; 5-gon: 5; 6-gon: 9; 7-gon: 14; 8-gon: 20. (ii) Increasing sides by 1 adds n – 1 diagonals. Formula: n(n – 3)/2, since each of the n vertices ...