Advertisements
Advertisements
प्रश्न
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following case, PQRS is a parallelogram?
∠P =85°, ∠Q = 85°, ∠R = 95°
Advertisements
उत्तर
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
∠P =85°, ∠Q = 85°, ∠R = 95°
By the angle sum property of a quadrilateral, we get:
∠P + ∠Q + ∠R + ∠S = 360
8585 + 95 + ∠S = 360
265 + ∠S = 360
∠S = 95
Clearly, ∠P ≠ ∠R
And ∠Q ≠ ∠S
Thus, we have PQRS a quadrilateral with opposite angles that are not equal.
Therefore,
PQRS is not a parallelogram.
APPEARS IN
संबंधित प्रश्न
ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D.
The following statement are true and false .
In a parallelogram, the diagonals are equal
The following statement are true and false .
In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.
The following statement are true and false .
If three sides of a quadrilateral are equal, it is a parallelogram .
The perimeter of a parallelogram is 22 cm. If the longer side measures 6.5 cm, what is the measure of shorter side?
In the given figure, ABCD and AEFG are two parallelograms. If ∠C = 58°, find ∠F.
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
The bisectors of the angle of a parallelogram enclose a
The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a
The figure formed by joining the mid-points of the adjacent sides of a rectangle is a
