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]
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]
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.
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.
