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Class 8 NCERT Solutions – Chapter 4 Practical Geometry – Exercise 4.1

  • Last Updated : 04 May, 2021

Question 1: Construct the following quadrilaterals:

(i) Quadrilateral ABCD
      AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm, AC = 7 cm

Procedure:

Given AB = 4.5 cm, BC = 5.5 cm, CD = 4 cm, AD = 6 cm, AC = 7 cm
We have to construct a quadrilateral ABCD

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  • Draw a rough sketch



  • Draw AB = 4.5 cm.
  • Taking B as centre, draw an arc of radius 5.5 cm.
  • Now taking A as the centre, draw an arc of radius 7 cm intersecting with the arc made previously with centre B. Mark the intersection point as point C. Join AC and BC, successively.
  • Taking A as the centre again, draw an arc of radius 6 cm.
  • Taking D as the centre (which was marked previously), draw an arc of radius 4 cm, now intersect both the arcs, one of radius 6 cm made from point A and the other made from point C, and mark the intersection point as D (update the rough point).
  • Now join AD and CD.
  • Hence we have the required quadrilateral ABCD.

(ii) Quadrilateral JUMP
       JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm

Procedure:

Given JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm
We have to construct a quadrilateral JUMP

  • Draw JU = 3.5 cm.
  • Taking J as centre draw an arc of radius 4.5 cm and taking U as centre draw an arc of 6.5 cm, such that both the arcs should intersect at point P. Join PJ and PU respectively.
  • Similarly, taking P and U as centre draw arcs of 5 cm and 4 cm respectively, intersect both the arcs at M.
  • Join MP and UM.
  • Hence we have the required quadrilateral.

(iii) Parallelogram MORE
        OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm

Procedure:

Given OR = 6 cm, RE = 4.5 cm, EO = 7.5 cm
We have to construct a parallelogram MORE (Opposite sides are equal in a parallelogram).

  • Draw an arc of 4.5 cm taking R as the centre.
  • Draw an arc of 7.5 cm taking O as the centre, such that it intersects the previous arc.
  • Join both the arcs at point E. Join EO and RE
  • Taking E as centre draw an arc of 6 cm.
  • Taking O as centre draw an arc of 4.5 cm.
  • Intersect both the arcs at M. Join EM and OM.
  • Therefore we have the required parallelogram MORE.

(iv) Rhombus BEST
        BE = 4.5 cm, ET = 6 cm

Procedure:

Given BE = 4.5 cm, ET = 6 cm
We have to construct a Rhombus BEST (all sides of a rhombus are equal)

  • Draw a triangle BET,

  • Draw ET = 6 cm.
  • Draw an arc of 4.5 cm from both the points E and T respectively, join BE and BT.
  • Similarly, taking E and T as centre draw arcs of 4.5 cm and intersect at S as shown below,

  • Join SE and ST.
  • Join Diagonal BE. Measure it will be 4.5 cm.
  • Therefore, we have the required Rhombus BEST.

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