If the midpoints of the sides of a Rectangle are joined in order, which of the following properties does the quadrilateral formed possess?
All sides are equal
By the midpoint (Varignon) theorem, joining the midpoints of the sides of any quadrilateral in order forms a parallelogram whose sides are parallel to, and half the length of, the diagonals of the original quadrilateral.
In a rectangle, both diagonals are equal in length, so the two pairs of sides of the resulting parallelogram (each being half of a diagonal) are also equal to each other — making all four sides of the new quadrilateral equal. Hence it is a rhombus. Answer: (A) All sides are equal.
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Important Questions from Quadrilaterals
The ratio between the length and breadth of a rectangular park is 3 : 2. If a man cycling along the boundary at the speed of 12 km per hour completes one round in 8 minutes, then the area of the park in square meter will be
A quadrilateral whose four sides and angles are equal to each other is known as
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PQRS is a cyclic quadrilateral. If ∠P is 4 times ∠R, and ∠S is 3 times ∠Q, then the average of ∠Q and ∠R is:
