Write the steps of construction of a parallelogram $A B C D$ in which diagonal $A C = 6.3 c m$ ; diagonal $B D = 7 c m$ and the acute angles between the diagonals is $45^{\circ}$ .

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Solution

$S t e p s$ $o f$ $c o n s t r u c t i o n :$
$S t e p 1 :$ Draw a line of length $6.3 c m$ .Mark it as $A C$
$S t e p 2 :$ Mark the point $O$ at mid point of $A C$
$S t e p 3 :$ With $O$ as center Draw a ray of angle $45$ degrees.
$S t e p 4 :$ Extend the ray on Both sides
$S t e p 5 :$ With $O$ as center draw the arcs of radius $3.5 c m$ on both sides
$S t e p 6 :$ Mark the points as $B$ and $D$ respectively and join the points

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60^{\circ}

60^{\circ}

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 C

B D

6.3 c m

7.0 c m

45^{o}

45^{\circ}

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