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Construction of Parallelogram When Two Adjacent Sides and One Diagonal Are Given.

Construct a p...

Question

Construct a parallelogram $A B C D$ such that $A C = 6 c m, B D = 4.6 c m$ and angle between them $45^{o}$ .

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Solution

Virtuoso
Construction: To draw a parallelogram ABCD
STEP I : Draw a line segment AC = 3.8 cm.
STEP II : Take a point O such that O is the midpoint of AC.
STEP III : With O as a point draw a line segment BD = 4.6 cm such that ∠COD = 60° and DO = OB = 2.3 cm.
STEP IV : Now join the points AB, BC, CD and DA.
Therefore we get a parallelogram ABCD.

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Similar questions

Construct a rhombus ABCD, with AC = 6 cm and BD = 4.6 cm. [4 MARKS]

A B C D

B C = 4.5 c m, B D = 4 c m

A C = 5.6 c m

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 $60^{\circ}$ .

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