exercise 11 above and a third using the centroid theorem – Discussion Forum

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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 ...