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

**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

- Draw a rough sketch

- Draw AB = 4.5 cm.
- Taking B as center, draw an arc of radius 5.5 cm.
- Now taking A as the center, draw an arc of radius 7 cm intersecting with the arc made previously with center B. Mark the intersection point as point C. Join AC and BC, successively.
- Taking A as the center again, draw an arc of radius 6 cm.
- Taking D as the center (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 center draw an arc of radius 4.5 cm and taking U as center 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 center 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 center.
- Draw an arc of 7.5 cm taking O as the center, such that it intersects the previous arc.
- Join both the arcs at point E. Join EO and RE
- Taking E as center draw an arc of 6 cm.
- Taking O as center 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 center 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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