Burst the bubbles in which the parameters are sufficient to construct a parallelogram-2-sides-1-angle2-side-1-diagonal1-side-1-diagonal2-diagonals2-side-1-Altitude2-diagonal-1angle1-side-1-diagonal2-sides amp-Area

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Standard VIII

Mathematics

Construction of Parallelogram Given Its Sides and Area

Burst the bub...

Question

Burst the bubbles in which the parameters are sufficient to construct a parallelogram.

2-sides
1-angle

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2-side
1-diagonal

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1-side
1-diagonal

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2-diagonals

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2-side
1-Altitude

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2-diagonal
1angle

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1-side
1-diagonal

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2-sides &
Area

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Name each of the following parallelograms :

(i) The diagonals are equal and the adjacent sides are unequal.

(ii) The diagonals are equal and the adjacent sides are equal.

(iii) The diagonals are unequal and the adjacent sides are equal.

(iv) All the sides are equal and one angle is $60^{\circ}$

(v) All the sides are equal and one angle is $90^{\circ}$

(vi) All the angles are equal and the adjacent sides are unequal.

Q. Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm. Measure the other side.

Q. Which of the quadrilaterals mentioned in brackets have the following properties?

(1) Diagonals are congruent. (square, rectangle, rhombus)
(2) The longer diagonal is the perpendicular bisector of the shorter and the shorter of the longer. (trapezium, kite, rhombus)
(3) All sides and angles are congruent. (rhombus, square, rectangle)
(4) Opposite angles are congruent. (kite, parallelogram, rectangle)
(5) Opposite sides are congruent. (trapezium, rectangle, parallelogram)
(6) Diagonals bisect each other at right angles. (square, rectangle, rhombus)
(7) Diagonals bisect each another. (rectangle, parallelogram, kite)
(8) One pair of opposite sides is parallel. (kite rhombus trapezium)

Q. Name the following parallelograms :
i) Adjacent sides are equal, diagonals are unequal.
ii) Adjacent sides are unequal, but adjacent angles are equal.
iii) The diagonals are equal and the adjacent sides are unequal.
iv) The diagonals intersect at right angle and adjacent sides are equal.
v) All sides are equal and diagonals are equal.
vi) Adjacent angles are equal, diagonals are equal, adjacent sides are unequal.

Adjacent sides of a parallelogram are equal and one of diagonals is equal to any one of the sides of this parallelogram. Show that its diagonals are in the ratio $\sqrt{3} : 1$ .

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