Construct a quadrilateral ABCD in which AB = BC = 6 cm, AD = DC = 4.5 cm and ∠B = 120°.

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Solution

$Steps of construction : Step I : Draw AB = 6 cm . Step II : Construct ∠ ABC = 120 ° . Step III : With B as the centre and radius 6 cm, cut off BC = 6 cm . Now, we can see that AC is about 10.3 cm which is greater than AD + CD = 4.5 + 4.5 = 9 cm . We know that sum of the lengths of two sides of triangle is always greater than the third side but here, the sum of AD and CD is less than AC . So, construction of the given quadrilateral is not possible .$

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Question 1
Construct the Quadrilateral ABCD where
AB=4.5 cm, BC=5.5 cm, CD=4 cm,AD=6cm, AC=7 cm

Construct a quadrliateral ABCD; if:

(i) AB = 4.3 cm, BC = 5.4, CD = 5 cm, DA = 4.8 cm and $∠$ ABC = $75^{\circ}$ .

(ii) AB = 6 cm, CD = 4.5 cm, BC = AD = 5 cm and $∠ BCD = 60^{\circ}$

(iii) AB = 8 cm, BC = 5.4 cm, AD = 6 cm, $∠ A = 60^{\circ}$ and $∠ B = 75^{\circ}$ .

(iv) AB = 5 cm, BC = 6.5 cm, CD = 4.8 cm, $∠ B = 75^{\circ}$ and $∠ C = 120^{\circ}$

(v) AB = 6 cm = AC, BC = 4 cm, CD = 5 cm and AD = 4.5 cm.

(vi) AB = AD = 5 cm, BD = 7 cm and BC = DC = 5.5 cm

A B C D

A B = 4 c m, B C = 5.6 c m, A C = 7.2 c m

A D = 4.5 c m

l (C D) = ?

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