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Question:

Construct the following quadrilaterals:
(i) Quadrilateral ABCD: AB=4.5cm, BC=5.5cm, CD=4cm, AD=6cm, AC=7cm
(ii) Quadrilateral JUMP: JU=3.5cm, UM=4cm, MP=5cm, PJ=4.5cm, PU=6.5cm
(iii) Parallelogram MORE: OR=6cm, RE=4.5cm, EO=7.5cm
(iv) Rhombus BEST: BE=4.5cm, ET=6cm

Solution:

1)Steps of construction:

  1. Draw AD of length 6 cm.
  2. Cut an arc of 7 cm from A and 4 cm from D. Their point of intersection is C.
  3. Cut an arc of 4.5 cm from A and 5.5 cm from C. Their point of intersection is B.
  4. Join all the points. ABCD is the required quadrilateral.

2)Steps of construction:

  1. Draw UM of length 4 cm.
  2. Cut an arc of 6.5 cm from U and 5 cm from M. Their point of intersection is P.
  3. Cut an arc of 3.5 cm from U and 4.5 cm from P. Their point of intersection is J.
  4. Join all the points. JUMP is the required quadrilateral.

3)Steps of construction:

  1. Draw OR of length 6 cm.
  2. Cut an arc of 7.5 cm from O and 4.5 cm from R. Their point of intersection is E.
  3. Cut an arc of 4.5 cm from O and 6 cm from E. Their point of intersection is M.
  4. Join all the points. MORE is the required parallelogram.

4)Steps of construction:

  1. Draw ET of length 6 cm.
  2. Draw its perpendicular bisector. [Draw the arcs with radius more than 6 cm at the centers E, T respectively above the line segment ET. which are intersects at a point. Similarly, draw the arcs with radius more than 6 cm at the centers E, T respectively below the line segment ET. which are intersects at another point. Join these two points of intersections of the arcs. Hence, the perpendicular bisector of ET formed.]
  3. Cut an arc of 4.5 cm from E on the perpendicular bisector both above and below ET, the points of intersections are B and S.
  4. Join all the points. BEST is the required rhombus.