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Constructions of Quadrillaterals

Constructions of Quadrillaterals

TGM Original Questions
  1. Construct a quadrilateral \(ABCD\) such that \(AB = 6.3\) cm, \(AC = 8.2\) cm, \(BD = 5.6\) cm, \(AB\) is perpendicular to \(BC\), and angle \(BAD = 60^\circ\).
    1. Measure and write down the largest possible size of angle \(ADC\).
    2. Construct a straight line parallel to \(AB\) that passes through \(C\) to meet \(AD\) produced at \(E\). Measure and write down the length of \(CE\) and determine the type of quadrilateral \(ABCE\).
  1. Construct a quadrilateral \(ABCD\) such that \(AB = 4.5\) cm, \(BC = 4\) cm, \(CD = 4.2\) cm, diagonal \(BD = 3.4\) cm, angle \(BAD = 40^\circ\) and angle \(ADB\) is acute.
    1. Measure and write down the length of \(AC\).
    2. Construct a point \(P\) that lies on side \(AD\), such that \(P\) is equidistant from \(A\) and \(B\). Measure and write down the length of \(PD\).

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Answer:(i)(a) \(154^\circ\). (i)(b) \(CE\approx3.3\text{ cm}\); trapezium. (ii)(a) \(AC\approx8.2\text{ cm}\). (ii)(b) \(PD\approx2.3\text{ cm}\), subject to drawing tolerance.

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