Jhon is constructing a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°. Can he complete the construction using the above given measurements?

Yes

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Yes, only if the length of one side is given.

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One more angle should be given.

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Solution

The correct option is A Yes
Steps of Construction:

1. Draw a line segment AC of length 3.8cm.

2. Construct a perpendicular bisector for AC to find the mid-point. mark the mid-point to be O.

3. From O, construct 60° and extend the line on both sides and mark X and Y respectively.

4. Find the length of BO and OD. BO = OD = 2.3cm .

5. Keeping O as the centre draw an arc of radius 2.3 cm on OX and OY.

6. Mark the intersecting point to be D and B respectively. Join A to B and D and C to B and D.

The following figure shows the parallelogram ABCD.

The construction is possible with the given measurements.

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Similar questions

Q. Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.

Q. Construction of quadrilaterals when three sides and two diagonals are given:
2. Construct a quadrilateral ABCD in which AB = 4 cm BC = 3.8 cm, AD = 3 cm, diagonal AC = 5 cm and diagonal BD = 4.6 cm.

Construct a parallelogram ABCD, if :

(i) AB = 3.6 cm, BC = 4.5 cm and $∠ ABC = 120^{\circ} .$

(ii) BC = 4.5 cm, CD = 5.2 cm and $∠ ADC = 75^{\circ} .$

(iii) AD = 4 cm, DC = 5 cm and diagonal BD = 7 cm.

(iv) AB = 5.8 cm, AD = 4.6 cm and diagonal AC = 7.5 cm.

(v) diagonal AC = 6.4 cm, diagonal BD = 5.6 cm and angle between the diagonals is $75^{\circ}$ .

(vi) lengths of diagonals AC and BD are 6.3 cm and 7.0 cm respectively, and the angle between them is $45^{\circ}$ .

(vii) lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively and the angle between then is $60^{\circ}$ .

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?

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