ML AGGARWAL CLASS 8 Chapter 14 Constructions of Quadrilaterals Exercise 14.2

May 29, 2021

Exercise 14.2

Question 1

Sol :

Steps.

1. Draw AB=5 cm

2. Draw $\angle B=120^{\circ}$ line and Cut it ar $\overline{B C}=3.2 \mathrm{cm}$, mark point ' c '

3.Draw $\angle A=\left(180^{\circ}-120^{\circ}\right)=60^{\circ}$ at Cut it at $\overline{AD}=$ 3.2cm , Mark point 'D'

4.Now join $\overline{D C}$, required quadrilateral ABCD formed.

Question 2

Sol :

Steps.

1. Draw AB=4.8 cm line

2 Draw B C =4cm Arc formed 'B'

3. Draw AD=BC=4 in Arc form A

4.Draw BD = 5.4cm are form B, intersection point 'D'

5.Join $\overline{ AD}$ and draw BC line parallel to AD intersection point is 'C'

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

Question 3

Sol :

Steps.

1.Draw BC = 4.5 cm

$B O=\frac{1}{2}(B D)=\frac{1}{2}(4)$=2 cm

$C O=\frac{1}{2}(A C)=\frac{1}{2}(56)=2.8 \mathrm{cm}$

$'O^{\prime}$ is formed.

2. Extend BO Such that BD=4 cm

3.Extend CO Such that AC= 5.6 cm

4. Now required parallelogram ABCD is formed

Question 4

Sol :

Steps.

1. Draw $A O=\frac{1}{2}(A C)$=3cm and produce AO to C such thus OC=OA

2. AO Construct $\angle A O P=45^{\circ}$

3.From OP, cut OB = 2.5cm , produced OB to D such thus OB = OD

4. Join $\overline{A D}, \overline{A B}, D \overline {C}, \overline{C D}$ ABCD parallelogram formed.

Question 5

Sol :

Steps.

1.Draw AB= 5.6cm

2.Draw $\angle B=90$ and BC = 4cm

3.Draw $\angle A=90$ and AD=BC=4C

4. Join $\overline$ DC , now rectangle ABCD is formed

Question 6

Sol :

Steps.

1. Draw AB=5 cm

Draw AO=BO=3.4 cm

2. Extend AO to C such that AC=6.8cm

Extend BO to D Such them BD=6.8 cm

3. Join $\overline{A D}, \overline{D C}, \overline{B C}$, Now rectangle ABCD is formed.

Question 7

Sol :

Steps.

1. Draw AB=4 cm

2. Draw $\angle BAC=90$ \& $\angle B 290^{\circ}$,

3. join $\overline{D C}$, A D, required rectangle ABCD is formed.

Question 8

Sol :

Steps.

1. AO=9.3 cm extend to C

Such that AO = OB

2. $\angle A O B=120^{\circ}$ and Draw BO=3.3 cm and external to D such then BO =OD

3. Join $\overline{A B}, \overline{B C}, \overline{C D}, \overline{A D}$, Now required rectangle ABCD is formed

Question 9

Sol :

Steps.

1.Draw AB = 5cm

2. At 'A' construct $\angle B A P=45^{\circ}$

3. From AP, cut off AD = 5cm

4.With B as centre and radius 5cm draw an arc

5.With D as centre and radius 5cm draw are meet radius arc at C

6. Join BC and CD Then ABCD a required rhombus

Question 10

Sol :

Steps.

1. Draw AB=4.5 cm

2. A as centre ,with 4.5cm radius draw arc

3. B as centre , with 5cm radius draw arc which meet previous arc at 'D'

4. With DC as centre with 4.5cm radius draw arcs they meet at 'C'

5. Join $\overlineAD, \overline\overline{D C}, \overline{B C}$, then A B C D is required rhombus

Question 11

Sol :

Steps

1. Draw AC=6.8 cm

2. Draw PQ, which perpendicular bisector of AC

3.Cut PQ such then OB= OD =2.6cm

4.Join $\overline{A B}, \quad \overline{B C},\overline{C D}, \overline{A D}$

Now ABCD is required rhombus.

Question 12

Sol :

Steps.

1. Draw AB=4.3 cm

2. $\angle A=90^{\circ}$ 'A' as centre, 4.4 cm radius draw arc , both meet at 'D'

3. Repeat the same at 'B' 'C' is Formed

4. Join AD, DC, BC , Now ABCD is required Square.

Question 13

Sol :

Steps.

1. Draw AC= 6.2 cm

2. Draw PQ , which is perpendicular bisector of AC

3. Cut PQ , from 'O ' Both sides such that OB = OD =3.1cm

4. Join AB,BC,CD, AD , Then ABCD is required square

ML Aggarwal Solution- myhelper.tk