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Construction of a Rectangle When One Diagonal and the Angle between the Two Diagonal Are Given.

One diagonal ...

Question

One diagonal = $6.0$ cm and the angle between the diagonals = $45^{\circ}$ .

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Solution

Steps :
(i) Draw AC = $6$ cm.
(ii) Draw right triangle ACB.
(iii) Draw right triangle ADB.
(iv) Join DC.
ABCD is the required rectangle.

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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 $60^{\circ}$ .

Construct a rectangle ABCD ; if :

(i) AB = 4.5 cm and BC = 5.5 cm.

(ii) BC = 6.1 cm and CD = 6.8 cm.

(iii) AB = 5.0 cm and diagonal AC = 6.7 cm.

(iv) AD = 4.8 cm and diagonal AC = 6.4 cm.

(v) each diagonal is 6 cm and the angle between them is $45^{\circ}$ .

(vi) each diagonal is 5.5 cm and the angle between them is $60^{\circ}$

45^{\circ}

6.0

3.5

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