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(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.

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(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 or construct a triangle where PQ serves as a median.

Class 9 Ganita Manjari part 2 Chapter 12 Solutions
Class 9 Ganita Manjari Part 2 Chapter 12 Page 79 Question Answer

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  1. (i) Since MB = DN and MB ∥ DN, MBND is a parallelogram, making MD ∥ BN. Let DM and BN intersect AC at X and Y. In △ABY, MX ∥ BY through midpoint M gives AX = XY. In △CDX, NY ∥ DX through midpoint N gives XY = YC, proving trisection: AX = XY = YC. (ii) 1. Complete a parallelogram on diagonal PQ. 2. Intercept three equal segments using parallel lines. 3. Construct a triangle with median PQ; the centroid trisects it in a 2:1 ratio.

     

    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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