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.
Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
