To construct a parallelogram ABCD- we are given the following data-AC -10 cm - BD -8 cm and - AOB -110-With these measurements- we can construct one and only one parallelogram-A- TrueB- False

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Constructing a Parallelogram When Its Two Diagonals and One Included Angle Are Given

To construct ...

Question

To construct a parallelogram ABCD, we are given the following data:
AC = 10 cm, BD = 8 cm and $∠ A O B = 110^{\circ} .$
With these measurements, we can construct one and only one parallelogram.

True

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False

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Solution

The correct option is A True
To construct a parallelogram, we draw a triangle with the
given measurements. Then, we find the fourth vertex using the measurements of the adjacent sides. Hence, three independent measurements are necessary to construct a parallelogram.
We are given the lengths of 2 diagonals and the angle between them, which is enough to construct a unique trapezium.

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Similar questions

We have a parallelogram ABCD with AC and BD as diagonals. In parallelogram ABCD, $∠$ ABC = $110^{\circ}$ , $∠$ DAC = $15^{\circ}$ , $∠$ CAB= $25^{\circ}$ , AB = 5cm, CD = 7cm. Can we construct this parallelogram?

We have a parallelogram ABCD with AC and BD as diagonals. In Parallelogram ABCD, $∠ A B C = 110^{\circ}$ , $∠ D A C = 15^{\circ}$ , $∠ C A B = 25^{\circ}$ , AB = 5 cm and CD = 7 cm. Can we construct this parallelogram?

We can construct an unique quadrilateral ABCD with AB = 4 cm, BC = 6 cm, AC = 7 cm, CD = 5 cm and BD = 8 cm.

Can we draw a quadrilateral ABCD with following measurements: AB = 3cm, BC = 5cm, AD = 4cm, CD= 7cm and BD=8cm?

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To construct a parallelogram ABCD, we are given the following data: AC = 10 cm, BD = 8 cm and ∠AOB=110∘. With these measurements, we can construct one and only one parallelogram.

To construct a parallelogram ABCD, we are given the following data:
AC = 10 cm, BD = 8 cm and $∠ A O B = 110^{\circ} .$
With these measurements, we can construct one and only one parallelogram.