1.

Arshad has five measurements of a quadrilateral ABCD. These are AB = 5 cm, ∠A = 50°, AC = 4 cm, BD = 5 cm and AD = 6 cm. Can he construct a unique quadrilateral? Give reasons for your answer.

Answer»

The quadrilateral ABCD with the given data cannot be constructed because of the following reasons :

  • If he takes diagonal BD first, then he is able to construct one ∆ABD but the second ABCD to complete the quadrilateral ABCD cannot be drawn as its only one side BD is known.
  • If he takes the diagonal AC first, then the construction of ∆ACP and ∆ABC is not possible as the data are insufficient.


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