Advertisements
Advertisements
Question
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following case, PQRS is a parallelogram?
OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm
Solution
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
OP = 6.5 cm, OQ = 6.5 cm, OR = 5.2 cm, OS = 5.2 cm
We know that the diagonals of a parallelogram bisect each other.
But, here we have
OP ≠ OR
And OQ ≠ OS
Therefore,
PQRS is not a parallelogram.
APPEARS IN
RELATED QUESTIONS
In ΔABC and ΔDEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see the given figure). Show that
(i) Quadrilateral ABED is a parallelogram
(ii) Quadrilateral BEFC is a parallelogram
(iii) AD || CF and AD = CF
(iv) Quadrilateral ACFD is a parallelogram
(v) AC = DF
(vi) ΔABC ≅ ΔDEF.
The following statement are true and false .
In a parallelogram, the diagonals are equal
The following statement are true and false .
In a parallelogram, the diagonals intersect each other at right angles .
The following statement are true and false .
If three sides of a quadrilateral are equal, it is a parallelogram .
The following statement are true and false .
If three angles of a quadrilateral are equal, it is a parallelogram .
In the given figure, ABCD and AEFG are two parallelograms. If ∠C = 58°, find ∠F.
If one angle of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is
In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC =
ABCD is a parallelogram and E and F are the centroids of triangles ABD and BCDrespectively, then EF =
The diagonals of a parallelogram ABCD intersect at O. If ∠BOC = 90° and ∠BDC = 50°, then ∠OAB =
