# Construct the following quadrilaterals.

(i) Quadrilateral ABCD, AB = 4.5 cm ,BC = 5.5 cm

CD = 4 cm, AD = 6 cm, AC = 7 cm

(ii) Quadrilateral JUMP, JU = 3.5 cm, UM = 4 cm

MP = 5 cm, PJ = 4.5 cm, PU = 6.5 cm

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

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

**Solution:**

- Based on the given information, the five given measurements are of 4 sides and one diagonal. When measurements of 4 sides and one diagonal of a quadrilateral is given, we can construct a quadrilateral (Page 58 of Grade 8 NCERT Book)
- Using the concept opposite sides of parallelogram are parallel and equal, the five measurements can be found.
- All sides of a rhombus are equal and opposite sides are parallel, measurements of all sides can be found.

(i) Quadrilateral ABCD

Let us first draw a rough sketch of quadrilateral.

Construction of quadrilateral can be done in two parts. First construct triangle ABC and then triangle ACD. Let us find based on given measurements whether it is possible to construct the triangles.

In ∆ABC,

5.5 + 4.5 > 7 and 5.5 - 4.5 < 7

7 + 4.5 > 5 and 7 - 4.5 < 5.5

5.5 + 7 > 4.5 and 7 - 5.5 < 4.5

It is possible to draw triangle ABC.

In ∆ACD

7 + 4 > 6 and 7 - 4 < 6

6 + 7 > 4 and 7 - 6 < 4

6 + 4 > 7 and 6 - 4 < 7

So, construction of triangle ACD is also possible.

Let us construct the quadrilateral.

Step 1: Draw line segment AB = 4.5 cm.

Step 2: With B as center and radius 5.5 cm draw an arc. With A as center and radius 7 cm draw another arc cutting the former arc.

Step 3: C is the intersecting point of arcs. Join BC and AC.

Step 4: Based on rough diagram, it is easy to find that AC is the diagonal. Therefore, the fourth vertex D should be on the opposite to B with reference to AC.

Step 3: With A as center and radius 6 cm draw an arc on the opposite side of point B. With C as center and radius 4 cm draw another arc cutting the former arc. D is the intersecting point of the arcs. Join AD and CD. ABCD is the required quadrilateral.

(ii) Quadrilateral JUMP

Step 1: Draw line segment JU = 3.5 cm.

Step 2: With J as center and radius 4.5 cm draw an arc. With U as center and radius 6.5 cm draw another arc cutting the former arc.

Step 3: P is the intersecting point of arcs. Join PJ and PU.

Step 4: Based on rough diagram, it is easy to find that PU is the diagonal. Therefore, the fourth vertex M should be on the opposite to J with reference to PU.

Step 3: With U as center and radius 4 cm draw an arc on the opposite side of point J. With P as center and radius 5 cm draw another arc cutting the former arc. M is the intersecting point of the arcs. Join PM and UM. JUMP is the required quadrilateral.

(iii) Parallelogram MORE

As we know that opposite sides of parallelogram are parallel and equal, the five measurements can be found.

ME = OR, MO = ER

Step 1: Draw a line segment OR = 6 cm.

Step 2: With R as radius and radius 4.5 draw an arc.

Step 3: With O as radius and radius 7.5 cm draw another arc cutting the former arc..

Step 4: E is the intersecting point. Join RE and OE.

Step 5: With E as centre and radius 6 cm draw an arc.

Step 6: With O as centre, draw another arc ad radius 4.5 cm cutting the former arc.at M.

Step 7: Join EM and OM.

Thus, MORE is the required parallelogram.

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

All sides of a rhombus are equal and opposite sides are parallel, measurements of all sides can be found.

Step 1: Draw a line segment ET = 6 cm.

Step 2: Taking E as centre and radius 4.5 cm, draw arcs on both sides of the line segment ET.

Step 3: Taking T as centre and radius 4.5 cm, draw arcs on both sides of the line segment ET cutting the former arcs.

Step 4: B and S are points of intersections of arcs.

Step 5: Join EB, ES, BT and TS.

Thus, BEST is the required rhombus.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 4

**Video Solution:**

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

NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.1 Question 1

**Summary:**

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

**☛ Related Questions:**

- Construct the following quadrilaterals. (i) Quadrilateral LIFT LI = 4 cm, IF = 3 cm TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm (ii) Quadrilateral GOLD OL = 7.5 cm, GL = 6 cm GD = 6 cm, LD = 5 cm, OD = 10 cm (iii) Rhombus BEND BN = 5.6 cm and DE = 6.5 cm.
- Construct the following quadrilaterals. (i) Quadrilateral MORE MO = 6 cm, OR = 4.5 cm ∠M = 60°, ∠O = 105°, ∠R = 105° (ii) Quadrilateral PLAN PL = 4 cm, LA = 6.5 cm ∠P = 90°, ∠A = 110°, ∠N = 85° (iii) Parallelogram HEAR HE = 5 cm, EA = 6 cm ∠R = 85° (iv) Rectangle OKAY OK = 7 cm, KA = 5 cm
- Construct the following quadrilaterals. (i) Quadrilateral DEAR DE = 4cm, EA = 5cm, AR = 4.5cm ∠E = 60°, ∠A = 90° (ii) Quadrilateral TRUE TR = 3.5cm, RU = 3cm, UE = 4cm ∠R = 75°, ∠U = 120°
- Draw the following. 1. A square READ with RE = 1 cm. 2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long. 3. A rectangle with adjacent sides of lengths 5 cm and 4 cm 4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

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