Prove that it is not possible to draw a quadrilateral ABCD with following measurements: $A B = 3 c m, B C = 5 c m, A D = 4 c m, C D = 7 c m$ and $B D = 8 c m$ ? [2 marks]

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Solution

If we have the measures of all the sides of a quadrilateral and its one diagonal, we can draw two triangles and hence, form a quadrilateral.

ABCD comprises of two triangle $△$ ADB & $△$ CDB (0.5 mark)
In Δ ADB, AB = 3cm, BD = 8cm, and AD = 4cm
Since, AB + AD $<$ BD

$△$ ADB can't be constructed. (1.5 mark)
So, quadrilateral ABCD can't be constructed.

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