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Question

# A football ground is in the shape of a rectangle. The ends of the centre line (EF) and the midpoints of the end lines (AB and CD) are joined to form a quadrilateral. Find the angle between the diagonals of the quadrilateral so formed? [3 MARKS]

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Solution

## Steps: 2 Marks Answer: 1 Mark Given that: ABCD is a rectangle. E and F are the mid-points of the lines AC and BD respectively. ∴AE=BF=EC=FD Also, AH=HB=CG=GD [ H is mid point of AB , G is midpoint of CD ] ∠A, ∠B, ∠C and ∠D are right angles. The four sides of rectangle formed i.e. EHFG will have equal dimensions. ∴The length of all their diagonals will also be same. EH=HF=FG=EG All sides of the quadrilateral are equal. So either it will be a Rhombus or a Square. But for both of these quadrilaterals, the diagonals intersect at a right angle. The angle formed between the diagonals is a right angle.

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