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प्रश्न
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
उत्तर
For ∠D + ∠B = 180°, quadrilateral ABCD may or may not be a parallelogram. Along with this condition, the following conditions should also be fulfilled.
The sum of the measures of adjacent angles should be 180º.
Opposite angles should also be of same measures.
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संबंधित प्रश्न
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
In the given figure, `square`PQRS and `square`ABCR are two parallelograms. If ∠P = 110° then find the measures of all angles of `square`ABCR.
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.
Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.
Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.
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°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
In the given figure, ABCD and BDCE are parallelograms with common base DC. If BC ⊥ BD, then ∠BEC = ______.
All rectangles are parallelograms.
Find the values of x and y in the following parallelogram.
In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
