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

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Can you draw a parallelogram BATS, where BA = 5 cm, AT = 6 cm and AS = 6.5 cm? Why?

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Can you draw a rhombus ZEAL, where ZE = 3.5 cm, diagonal EL = 5 cm? Why?

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A student attempted to draw a quadrilateral PLAY, where PL = 3 cm, LA = 4 cm, AY = 4.5 cm, PY = 2 cm and LY = 6 cm but could not draw it. What is the reason?

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Can we draw the quadrilateral by drawing \(\Delta \) ABD first and then find the fourth point C?

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Can you construct a quadrilateral PQRS with PQ = 3 cm,RS = 3 cm, PS = 7.5 cm, PR = 8 cm and SQ = 4 cm?Justify your answer

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Can you construct the above quadrilateral MIST, if we have 100° at M instead of 75°?

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Can you construct the quadrilateral PLAN, if PL = 6 cm, \(\angle \)A = 9.5 cm, \(\angle \)P = 75°, \(\angle \)L = 150° and \(\angle \)A = 140°?

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

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Is it possible to construct a quadrilateral ABCD in which AB = 3 cm, BC = 5 cm, \(\angle \)B = 120°, \(\angle \)C = 105°, \(\angle \)A = 160°? If not, why?

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Is it possible to construct a quadruaterat MATH in which MA = 3 cm, AT = 5 cm, TH = 6 cm, HM = 4 cm and diagonal MT = 9 cm? If not, why?

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Can you construct the quadrilateral MIST, if we have 100° at \(\angle \)M instead of 75°. In the quadrilateral MIST, where MI = 3.5 cm, IS = 6.5 cm, \(\angle \)M = 75°, \(\angle \)I = 105° and \(\angle \)S = 120°?

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Can you construct the quadrilateral PLAN, if PL = 6 cm, LA = 9.5 cm, \(\angle \)P = 75°, \(\angle \)L = 150° and \(\angle \)A = 140°?

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In a parallelogram, the lengths of adjacent sides are known. Do we still need measures of the angles to construct?

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In a parallelogram, the lengths of adjacent sides are known. Do we still need measures of the angles to construct as in the Q-1 above?

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(a)