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Piyush365

Asked: October 5, 2026In: Class 9 Maths

Is the Midpoint Theorem for Quadrilaterals (Theorem 9) true when the quadrilateral is non-convex? How about when it is self-intersecting? Experiment and check. The pictures may look strange, but the theorem appears to be true. (i) Can you explain why this is so? See the geometric reasoning in the text. (ii) There is one exception: In a very special case the Varignon parallelogram becomes a single segment. When will this happen? (iii) Does your reasoning apply even when ABCD is non-planar?

Yes, it holds in both cases. (i) The Midpoint Theorem on triangles formed by diagonals still ensures opposite sides are parallel and equal to half the diagonal. (ii) It degenerates into a segment when diagonal AC is parallel to BD ...

Piyush365

Asked: October 5, 2026In: Class 9 Maths

(i) Suppose ABCD is a parallelogram and M, N are midpoints of AB and CD respectively. Show that segments DM and BN trisect segment AC. (ii) Use part (i) to find a procedure to trisect any given segment PQ. Find two other ways to trisect PQ, one using Exercise 11 above and a third using the Centroid Theorem.

(i) MBND is a parallelogram, so MD ∥ BN. Applying Theorem 7 to △ABY and △CDX proves the intercepts along AC are equal. (ii) Construct a parallelogram with diagonal PQ, draw parallel lines dividing an auxiliary ray into three parts ...

Piyush365

Asked: October 5, 2026In: Class 9 Maths

A farm has some cows, sheep and chickens. Last year the cows made up 60%, the sheep 25% and the chickens 15%. There was a decrease in the number of all three animals’ population over the year. Choose the possibilities for the change in their respective shares of the population— (i) % of cows decreased, % of sheep decreased, % of chickens decreased (ii) % of cows increased, % of sheep increased, % of chickens increased (iii) % of cows remained the same, % of sheep remained the same, % of chickens remained the same (iv) % of cows decreased, % of sheep increased, % of chickens remained the same (v) % of cows increased, % of sheep increased, % of chickens decreased.

Possibilities (iii), (iv) and (v) are possible. The sum of percentage shares must always equal 100%, so all shares cannot simultaneously increase or simultaneously decrease together, ruling out (i) and (ii). Class 9 Ganita Manjari Part 2 Chapter 10 Solutions Class ...

Piyush365

Asked: October 5, 2026In: Class 9 Maths

Given some data with corresponding weights, what would happen to the weighted average if all the weights are increased by a constant value, say 1? If required, experiment with some data. What do you observe? Justify your answer using algebra.

The weighted average shifts closer to the simple arithmetic mean. Adding 1 to each weight reduces relative differences between weights, diminishing the dominant impact of originally heavy-weighted values. CBSE released Class 9 Ganita Manjari Part 2 book and Solutions Class 9 ...

Piyush365

Asked: October 5, 2026In: Class 9 Maths

Whole class project: Each student shares the average age of their family and the number of family members. Discuss among the class and come up with a way to find out the average age of all the families of the class.

Multiply each student’s family average age by their family size to find total family years. Sum these values and divide by total members across all families for the combined mean. Class 9 maths Chapter 10 How Quantities Combine Understanding Data solutions

Given some data with corresponding weights, what would happen to the weighted average if all the weights are increased by a constant value, say 1? If required, experiment with some data. What do you observe? Justify your answer using algebra.

Whole class project: Each student shares the average age of their family and the number of family members. Discuss among the class and come up with a way to find out the average age of all the families of the class.

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