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In quadrilateral ABCD, P, Q, R, S are mid-points of AB, BC, CD, DA. If ABCD has diagonals AC = BD = 10 cm, what shape is PQRS and what is the length of each of its sides?

Class 9The Mid-point TheoremGeometry — Quadrilaterals
  • Arhombus, side 5 cm
  • Brectangle, side 5 cm
  • Csquare, side 10 cm
  • Dparallelogram, side 10 cm

Step-by-Step Solution

Each side of PQRS is half a diagonal = 5 cm. Since both diagonals are equal, all four sides are equal, making PQRS a rhombus with side 5 cm.
Answer: A) rhombus, side 5 cm

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