Question

construct a quadrilateral ABCD in which BC is equal to 5 cm CD is equal to 4 cm angle is equal to 60 degree angle b is equal to 120 degree angle d is equal to 95 degree measure AC and BD

Answer 1

  Construct the following quadrilaterals:

      (i)   Quadrilateral ABCD

      (ii)  Quadrilateral JUMP

               AB = 4.5 cm

JU = 3.5 cm

               BC = 5.5 cm

UM = 4 cm

               AD = 4 cm

MP = 5 cm

               AD = 6 cm

PJ = 4.5 cm

               AC = 7 cm

PU = 6.5

      (iii) Parallelogram MORE

      (iv) Rhombus BEST

               OR = 6 cm

BE = 4.5 cm

               RE = 4.5 cm

ET = 6 cm

               EO = 7.5 cm

Sol.   (i)   First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown. We may divide it into two conveniently constructible Δs ABC and ACD.

               

            Steps of construction:

            1.   Draw AC = 7 cm.

            2.   With A as centre and radius 4.5 cm, draw an arc (below AC).

            3.   With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.

               

            4.   Join AB and BC

            5.   With A as centre and radius 6 cm, draw an arc (above AC).

            6.   With C as centre and radius 4 cm, draw another arc cutting the previous arc and D.

            7.   Join AD = CD.

            Then, ABCD is the required quadrilateral.

            (ii)  First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.

               

            We may divide it inot two conveniently constructible Δs PJU and PMU.

               

            Steps of construction:

            1.   Draw PU = 6.5 cm

            2.   With P as centre and radius 4.5 cm, draw an arc(below (PU)