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प्रश्न
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
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उत्तर
AC = BD (Given)
& AC ⊥ BD (Given)
i.e. Diagonals of a quadrilateral are equal and they are ⊥ to each other.
∴ ABCD is square.
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संबंधित प्रश्न
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?
In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square`PQRS is a parallelogram.
In the adjacent figure, if seg AB || seg PQ, seg AB ≅ seg PQ, seg AC || seg PR, seg AC ≅ seg PR then prove that, seg BC || seg QR and seg BC ≅ seg QR.
PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.
Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
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(vi) ABCD is a rectangle
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If opposite angles of a quadrilateral are equal, it must be a parallelogram.
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The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45°. Find the angles of the parallelogram.
In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
