Length of diagonals $A C$ and $B D$ are $6.3 c m$ and $7.0 c m$ respectively, and the angle between them is $45^{o}$ construct a paralleogram.

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Solution

The Construction is as shown in the figure. Below are the steps.

1. Draw $A C = 6.3 c m$

2. Bisect $A C$ at $O$

3. At $O$ , draw $∠ X O C = 45^{\circ}$ and produce $X O$ to $Y$

4. Cut $O B = O D = 3.5 c m$ (half the diagonal $7 c m$ )

5. Join $A B, C B, A D$ and $C D$ . Thus $A B C D$ is the required parallelogram.

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Similar questions

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 $60^{\circ}$ .

A B C D

A C = 6.3 c m

B D = 7 c m

45^{\circ}

A B C D

A C = 6 c m, B D = 4.6 c m

45^{o}

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