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Piyush365
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Asked: 2026-10-05T09:33:59+00:00 In:

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?

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(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 connects to n – 3 non-adjacent vertices.

Cbse Class 9 Maths Ganita Manjari Part 2 Solutions
class 9 maths ganita manjari part 2 chapter 12 question answer

can you guess a formula for the number of diagonalsfind a pattern and guess the answers for n = 7 and n = 8ganita manjari part 2 chapter 12 quadrilaterals solutionsganita manjari part 2 chapter 12 question answerquadrilaterals solutions – ganita manjari part ii chapter 12should we define a diagonal of an n-gon
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    1. (i) A diagonal is a straight line segment joining any two non-consecutive vertices. Counts: 3-gon has 0; 4-gon has 2; 5-gon has 5; 6-gon has 9; 7-gon has 14; 8-gon has 20 diagonals.

      (ii) Adding one vertex introduces n – 1 new diagonals. Formula: n(n – 3)/2. Justification: Each of the n vertices can connect to n – 3 non-adjacent vertices (excluding itself and its two neighbors). Multiplying gives n(n – 3) and dividing by 2 avoids double-counting each segment.

       

      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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