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°
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
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
The following statement are true and false.
In a parallelogram, the diagonals bisect each other.
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 all the angles of a quadrilateral are 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 following statement are true and false .
If three angles of a quadrilateral are equal, it is a parallelogram .
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 figure formed by joining the mid-points of the adjacent sides of a rectangle is a
ABCD is a parallelogram, M is the mid-point of BD and BM bisects ∠B. Then ∠AMB =
ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF =
