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We have identified different types of quadrilaterals—squares, rectangles, parallelograms, rhombi, kites and trapezia. One can identify more types (e.g., we could create a category of quadrilaterals that have equal-length opposite sides). Suppose we have identified a category of quadrilaterals called Q and we have to construct a quadrilateral of this type. For this, we are to use two thin sticks, put them together as diagonals so that the quadrilateral obtained by joining their endpoints is of type Q (see the Fig. 9.2). (i) Suppose Q satisfies the following property. If a quadrilateral is of type Q, then it has equal-length diagonals. (a) Should the two sticks be of equal length? Why or why not? (b) Will it matter how the two sticks are put together? (ii) Instead of the property mentioned above, suppose Q satisfies the following property. If a quadrilateral has equal diagonals, then it is of type Q. What will be your answers to (a) and (b) now?

In (i), the sticks must be equal and their arrangement matters because equal diagonals alone do not guarantee type Q. In (ii), equal sticks arranged in any manner guarantee type Q. Class 9 Maths Ganita Manjari Part 2 All Chapter Solutions

cbse class 9 maths ganita manjari part 2 solutionsclass 9 ganita manjari part 2 chapter 9 propositions and their converses solutionsclass 9 maths ganita manjari part 2 chapter 9 question answeridentified different types of quadrilateralsshould the two sticks be of equal lengthsuppose q satisfies the following property
Piyush365
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Proposition: If a number is divisible by 3, then the sum of its digits is a multiple of 3. Converse: If the sum of the digits is a multiple of 3, then the number is divisible by 3. Cbse Class 9 ...

class 9 ganita manjari part 2 chapter 9 page 6 question answerexpress the relationship between 'a number is divisible by 3ganita manjari part 2 chapter 9 solutionssum of the digits is a multiple of 3
Piyush365
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The statement holds because 2 and 4 divide 8. However, checking 2 and 4 is not enough for 8; for instance, 12 is divisible by both 2 and 4, but not 8. Class 9 Maths Ganita Manjari Part 2 chapter 9 ...

a number is divisible by 8divisibility shortcuts that we have studied for different numbersdivisible by 2 and 4ganita manjari part 2 chapter 9 propositions and their converses solutionsganita manjari part 2 chapter 9 question answerncert solutions – ganita manjari part ii propositions and their converses
Piyush365
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For (i), n = 11 is prime, but 2¹¹ − 1 = 2047 = 23 × 89 is composite. For (ii), n = 6 is even, but 2⁶ + 1 = 65 = 5 × 13 is composite. Class 9 Maths ...

cbse released class 9 ganita manjari part 2 bookdownload class 9 maths ganita manjari part 2 book and solutionsganita manjari part 2 solutions available!if n is an even numbern is a prime numberthen 2ⁿ + 1 is a prime number
Piyush365
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Counterexamples disprove all three: for (i), n = 4 gives 4(16) + 1 = 65 = 5 × 13; for (ii), n = 10 gives 121 = 11²; for (iii), n = 3 gives 67? No, n = 2 gives ...

all numbers of the form 4n² + 1 are primecbse class 9 maths ganita manjari part 2 solutionsclass 9 ganita manjari part 2 chapter 9 propositions and their converses solutionsclass 9 maths ganita manjari part 2 chapter 9 question answercounterexamples to the following claims
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