Exercise 14.1
Question 1
(diagram should be added)
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 quadrilature PQRS formed
Question 2
(diagram should be added)
Steps.
1. Dract $A B=3.5 \mathrm{Cm}$
2. From 'A' draw Are $A D=5 \mathrm{Cm}$
3.From 'B' draw Arc BD = 5.4cm , Intersection point is 'D'
4. From $B^{\prime}$ draw Are $B C=5 \mathrm{~cm}$.
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
(diagram should be added)
Steps.
1. Draw $P Q=3 \mathrm{~cm}$ 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
(diagram should be added)
Steps.
1.Draw $A B=5 \mathrm{~cm}$ 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 fromed.
Question 5
(diagram should be added)
Steps.
1. Draw $B C=6 \mathrm{~cm}$ line
2. At 'C' Draw C= 90 line upto $\overline{DC}=4 \mathrm{~cm}$ nuric 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
(diagram should be added)
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
(diagram should be added)
Steps.
1. Draw $A B=5 \mathrm{Cm}$ 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
(diagram should be added)
Steps.
1. Draw PQ= $4 \mathrm{~cm}$ 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 $R S=$\amgle 4.5 \mathrm{~cm}$
4.Now Join $\overline PS$ Now required quadrilateral PQRS formed.
Question 9
(diagram should be added)
Steps.
1. Draw $B E=3.8 \mathrm{~cm}$ line
2. Draw $\angle E=80^{\circ}$, and an arc $E S=3.4 \mathrm{~cm}$ 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
(diagram should be added)
Steps.
1. Draw $A B=4.5 \mathrm{~cm}$ 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.
Exercise 14.2
Question 1
(diagram should be added)
Steps.
1. Draw $A B=5 \mathrm{Cm}$
2. Draw $\angle B=120^{\circ}$ line and Cut it ar $\overline{B C}=3.2 \mathrm{Cm}$, merk 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 qudrilateral $A B C D$ formed.
Question 2
(diagram should be added)
Steps.
1. Draw AB=4.8 $\mathrm{~cm}$ line
2 Draw B C =4cm Arc formed 'B'
3. Draw $A D=B C=4$ im Are 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
(diagram should be added)
Steps.
1.Draw Bc = 4.5 cm
$B O=\frac{1}{2}(B D)=\frac{1}{2}(4)=2 \mathrm{~cm}$
$C O=\frac{1}{2}(A C)=\frac{1}{2}(56)=2.8 \mathrm{Cm}$
$'O^{\prime}$ is formed.
2. Extend Bo Such that $B D=4 \mathrm{~cm}$
3.Extend CO Such that AC= 5.6cm
4. Now required parallelogram ABCD is formed
Question 4
(diagram should be added)
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
(diagram should be added)
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
(diagram should be added)
Steps.
1. Draw $A B=5 \mathrm{~cm}$
Draw $A O=B O=3.4 \mathrm{~cm}$
2. Extend AO to C such tas $A C=6.8 \mathrm{~cm}$
Extend $B O$ to $D$ Such them $B D=6.8 \mathrm{~cm}$
3. Join $\overline{A D}, \overline{D C}, \overline{B C}$, Now rectangle ABCD is formed.
Question 7
(diagram should be added)
Steps.
1. Draw $A B=4 \mathrm{~cm}$
2. Draw $\angle B A C=90$ \& $\angle B 290^{\circ}$,
3. join $\overline{D C}, A D$, required rectangle $A B C D$ is formes.
Question 8
(diagram should be added)
Steps.
1. $A O=9.3 \mathrm{~cm}$ extend to C
Such that AO = OB
2. $\angle A O B=120^{\circ}$ and DrAW $B O=3.3 \mathrm{~cm}$ 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
(diagram should be added)
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. Joion BC and CD Then ABCD a required rohmbus
Question 10
(diagram should be added)
Steps.
1. Drau $A B=4.5 \mathrm{~cm}$
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 rohmbus
Question 11
(diagram should be added)
Steps
1. Draw $A C=6.8 \mathrm{~cm}$
2. Draw PQ, which perpendicular bisectornof $A C$
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
(diagram should be added)
Steps.
1. Draw $A B=4.3 \mathrm{Cm}$
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
(diagram should be added)
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
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