Q2. We used some five measurements to draw quadrilaterals so far. Can there be different sets of five measurements (other than seen so far) to draw a quadrilateral? The following problems may help you in answering the question.

(i) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and \angle B = 80\degree.

(ii) Quadrilateral PQRS with PQ = 4.5 cm, \angle P = 70\degree, \angle Q = 100\degree, \angle R = 80\degree
and \angle S = 110\degree.

Construct a few more examples of your own to find sufficiency/insufficiency of the
data for the construction of a quadrilateral.

Answers (1)

Yes, there can be other sets of five measurements to draw a quadrilateral.

Examples:

(i)  Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm and \angle B = 80\degree.  (GIVEN)

            (All 4 sides and 1 angle)

(ii) Quadrilateral PQRS having PQ = 4.5 cm, \angle P = 70\degree, \angle Q = 100\degree, \angle R = 80\degree
and \angle S = 110\degree.

            (1 side, all 4 angles)

(iii) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, CD = 4 cm, BD = 8 cm  (Included angle diagonal)  and \angle B = 80\degree.

            (3 sides, 1 included angle, and included angle diagonal)

(iv) Quadrilateral ABCD with AB = 5 cm, BC = 5.5 cm, BD = 8 cm ,\angle B = 80\degree and \angle C = 95\degree

            (2 sides, 2 angles (1 included), and included angle diagonal).

There can be plenty of other examples.

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