ML AGGARWAL CLASS 8 Chapter 14 Constructions of Quadrilaterals Exercise 14.1

 Exercise 14.1

Question 1

Sol :

Steps.

1. Draw PQ = 4.5cm

2.From Q draw are of length 6cm

3.From p draw are of length 6.5cm, intersection point is 'R'

4.From R draw are of length 5.5cm

5.From P draw are of the length 5cm , Intersection point is 'S'

6.Join $\overline{\mathrm{Q} R }, \overline{\mathrm{SR}}_{ ,} \overline{\mathrm{PS}}$, required quadrilateral PQRS formed

Question 2

Sol :

Steps.

1. Draw AB=3.5 cm

2. From 'A' draw Arc AD=5 cm

3.From 'B'  draw Arc BD = 5.4cm , Intersection point is 'D'

4. From $B^{\prime}$ draw Arc BC=5 cm

5.From 'D' draw arc DC = 5.6 cm , Intersection Point is 'C'

6.Join $\overline{A D}, \overline{D C}, \overline{B C}$ The required quadrilateral ABCD is formed

Question 3

Sol :

Steps.

1. Draw PQ=3 cm line

2.From Q , draw arc QR 2.2cm

3.From P , draw arc PR = 4CM , Intersection Point is 'R'

4.From  Q , draw arc QS = 5CM

5. From P, Draw arc PS = 3.5 CM , Intersection point is 'S'

6.Join $\overline{Q R}$, $\overline{P S}_{,} \overline{S R}$, Now required quadrilateral is formed

Question 4

Sol :

Steps.

1.Draw AB=5 cm line

2.From 'A' draw AC =7cm

3.From 'B' draw arc BC = 5.5 cm , Intersection point 'C'

4.From 'A' draw Arc AD = 5.5 cm

5. From 'C' draw Arc CD = 4.5 cm , Intersection point 'D'

6. Join $\overline{B C}, \overline{D L}, \overline{A D}$, Now required quadrilateral ABCD formed.

Question 5

Sol :

Steps.

1. Draw BC=6 cm line

2. At 'C' Draw C= 90 line upto $\overline{DC}=4 \mathrm{~cm}$ name point 'D'

3. From 'B' Draw $\angle B=45^{\circ}$ line 

4. From 'D' draw $\angle D=120^{\circ}$ Line , Intersection point is 'C '

5. Join $\overline{B C}, \overline{C D}$ Now required quadrilateral ABCD formed.

Question 6

Sol :

Steps.

1.Draw PQ = 4cm line 

2. Draw $\angle$ Q = 90 line up $\overline QR$= 6cm and mark 'R'

3.Draw $\angle P 60^{\circ}$ line

4.Draw $\angle$ R=120 line , Intersection Point is 'S'

5. Join $\overline{\mathrm{PS}}, \overline{\mathrm{SR}}$, Now required quadrilateral PQRS formed

  

Question 7

Sol :

Steps.

1. Draw AB=5 cm line

2. Draw $\angle B=60^{\circ}$ line from $B^{\prime}$

3.Draw Cut $\angle B=60^{\circ}$ Line with Arc of BC = 4.2 cm point 'C'

4.At 'A' Draw $\angle A=90$ and at a distance of AD = 3.5cm mark 'D'

5.Join $\overline{D C}$ Now required quadrilateral ABCD is formed.

Question 8 

Sol :

Steps.

1. Draw PQ= 4 cm line

2.Draw $\angle Q=60^{\circ}$ line and at from Q, draw arc of QR = 5cm

3.Draw $\angle R=90^{\circ}$ line upto a distance $R S=$\angle$ 4.5 cm

4.Now Join $\overline PS$ Now required quadrilateral PQRS formed.

Question 9

Sol :

Steps.

1. Draw BE=3.8 cm line

2. Draw $\angle E=80^{\circ}$, and an arc ES=3.4 cm and both cut at point 's'

3. Draw ST= 4.5 cm arc from 'S'

4. Draw BT = 5cm Arc from 'B' and Intersection Point 'T'

5. Now join $\overline{B C}, \overline{T S}$ required quadrilateral BEST formed.

Question 10

Sol :

Steps.

1. Draw AB=4.5 cm line

2.Draw  $\angle B=60^{\circ}$ line From 'B' and draw an arc BC = 4cm from 'B' Intersection Point is 'C'

3. Draw arc Dc = 3.9 cm From 'C'

4. Draw arc AD =3.2 cm from 'A' Intersection Point 'D'

5.Join $\overline{C D}, \overline{A D}$ , Now required quadrilateral ABCD formed.