copy only pqrs on another paper – Discussion Forum

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Kiara Singh

Asked: October 1, 2026In: Class 9 Maths

Suppose PQRS is the Varignon parallelogram of ABCD. (i) Copy only PQRS on another paper. Show how you will recreate a congruent copy A’B’C’D’ of ABCD from PQRS. This will be relevant when we return to study tilings at the end of this chapter. (Hint: How will you place vertex A’? How will you place B’, C’ and D’?) (ii) There are multiple ways to construct A’B’C’D’ in (i). Justify why the quadrilateral A’B’C’D’ you constructed is congruent to ABCD. You may need to show why S is collinear with the points A’ and D’ that you constructed and similarly for P, Q and R. (Hint: Use congruence of triangles, for example △SDR ≅ △SD’R.) (iii) Show that if PQRS is a square, then AC and BD are perpendicular and equal. Prove the converse.

(i) Reconstruct corner △A’PS ≅ △APS, then extend A’P through P to get B’ and continue similarly for C’, D’. (ii) Point reflections across midpoints ensure collinearity and matching lengths. (iii) A square has equal, perpendicular sides; since sides equal ...