Class 8 Exam > Class 8 Notes > Mathematics (Maths) Class 8 > Construction of Quadrilaterals
Construction of Quadrilaterals | Mathematics (Maths) Class 8 PDF Download
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Page 1
Q u e s t i o n : 1
Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 4. 2 cm
.
Step 2: With A as the centre and radius equal to 8 cm
, draw an arc.
Step 3: With B as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to 5 cm,
draw an arc.
Step 6: With C as the centre and radius equal to 5. 2 cm
, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 2
Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ = 5. 4 cm
.
Step 2: With P as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With Q as the centre and radius equal to 4. 6 cm
, draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to 3. 5 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 4. 3 cm
, draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 3
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 5 cm
.
Step 2: With B as the centre and radius equal to 5. 6 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 4. 5 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to 4. 5 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 8 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Page 2
Q u e s t i o n : 1
Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 4. 2 cm
.
Step 2: With A as the centre and radius equal to 8 cm
, draw an arc.
Step 3: With B as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to 5 cm,
draw an arc.
Step 6: With C as the centre and radius equal to 5. 2 cm
, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 2
Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ = 5. 4 cm
.
Step 2: With P as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With Q as the centre and radius equal to 4. 6 cm
, draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to 3. 5 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 4. 3 cm
, draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 3
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 5 cm
.
Step 2: With B as the centre and radius equal to 5. 6 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 4. 5 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to 4. 5 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 8 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 4
Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 6 cm
.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 2. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 4. 6 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 5
Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.
S o l u t i o n :
Steps of construction:
Step 1: Draw QR = 7. 5 cm.
Step 2: With Q as the centre and radius equal to 10 cm
, draw an arc.
Step 3: With R as the centre and radius equal to 5 cm
, draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to 6 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 6
construct a quadrilateral ABCD in which AB =3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 4 cm.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 5. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 8 cm,
draw an arc.
Step 6: With D as the centre and radius equal to 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 7
Page 3
Q u e s t i o n : 1
Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 4. 2 cm
.
Step 2: With A as the centre and radius equal to 8 cm
, draw an arc.
Step 3: With B as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to 5 cm,
draw an arc.
Step 6: With C as the centre and radius equal to 5. 2 cm
, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 2
Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ = 5. 4 cm
.
Step 2: With P as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With Q as the centre and radius equal to 4. 6 cm
, draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to 3. 5 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 4. 3 cm
, draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 3
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 5 cm
.
Step 2: With B as the centre and radius equal to 5. 6 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 4. 5 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to 4. 5 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 8 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 4
Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 6 cm
.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 2. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 4. 6 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 5
Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.
S o l u t i o n :
Steps of construction:
Step 1: Draw QR = 7. 5 cm.
Step 2: With Q as the centre and radius equal to 10 cm
, draw an arc.
Step 3: With R as the centre and radius equal to 5 cm
, draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to 6 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 6
construct a quadrilateral ABCD in which AB =3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 4 cm.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 5. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 8 cm,
draw an arc.
Step 6: With D as the centre and radius equal to 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 7
Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ?ABC = 120°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 3. 5 cm
.
Step 2: Make ?ABC = 120
°
.
Step 3: With B as the centre, draw an arc 3. 5 cm
and name that point C.
Step 4: With C as the centre, draw an arc 5. 2 cm
.
Step 5: With A as the centre, draw another arc ?5. 2 cm
, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, ABCD
is the required quadrilateral.
Q u e s t i o n : 8
Construct a quadrilateral ABCD in which AB = 2.9 cm, BC = 3.2 cm, CD = 2.7 cm, DA = 3.4 cm and ?A = 70°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 2. 9cm
Step 2: Make ?A = 70
°
Step 3: With A as the centre, draw an arc of 3. 4cm
. Name that point as D.
Step 4: With D as the centre, draw an arc of 2. 7cm
.
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 9
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ?B = 125° and ?C = 60°.
S o l u t i o n :
Steps of construction:
Step 1: Draw BC= 5cm
Step 2: Make ?B = 125
°
and ?C = 60
°
Step 3: With B as the centre, draw an arc of 3. 5 cm
. Name that point as A.
Step 4: With C as the centre, draw an arc of 4. 6 cm
. Name that point as D.
Step 5: Join A and D.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 1 0
Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ?Q = 45° and ?R = 90°.
S o l u t i o n :
Steps of construction:
Page 4
Q u e s t i o n : 1
Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 4. 2 cm
.
Step 2: With A as the centre and radius equal to 8 cm
, draw an arc.
Step 3: With B as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to 5 cm,
draw an arc.
Step 6: With C as the centre and radius equal to 5. 2 cm
, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 2
Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ = 5. 4 cm
.
Step 2: With P as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With Q as the centre and radius equal to 4. 6 cm
, draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to 3. 5 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 4. 3 cm
, draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 3
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 5 cm
.
Step 2: With B as the centre and radius equal to 5. 6 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 4. 5 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to 4. 5 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 8 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 4
Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 6 cm
.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 2. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 4. 6 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 5
Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.
S o l u t i o n :
Steps of construction:
Step 1: Draw QR = 7. 5 cm.
Step 2: With Q as the centre and radius equal to 10 cm
, draw an arc.
Step 3: With R as the centre and radius equal to 5 cm
, draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to 6 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 6
construct a quadrilateral ABCD in which AB =3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 4 cm.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 5. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 8 cm,
draw an arc.
Step 6: With D as the centre and radius equal to 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 7
Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ?ABC = 120°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 3. 5 cm
.
Step 2: Make ?ABC = 120
°
.
Step 3: With B as the centre, draw an arc 3. 5 cm
and name that point C.
Step 4: With C as the centre, draw an arc 5. 2 cm
.
Step 5: With A as the centre, draw another arc ?5. 2 cm
, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, ABCD
is the required quadrilateral.
Q u e s t i o n : 8
Construct a quadrilateral ABCD in which AB = 2.9 cm, BC = 3.2 cm, CD = 2.7 cm, DA = 3.4 cm and ?A = 70°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 2. 9cm
Step 2: Make ?A = 70
°
Step 3: With A as the centre, draw an arc of 3. 4cm
. Name that point as D.
Step 4: With D as the centre, draw an arc of 2. 7cm
.
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 9
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ?B = 125° and ?C = 60°.
S o l u t i o n :
Steps of construction:
Step 1: Draw BC= 5cm
Step 2: Make ?B = 125
°
and ?C = 60
°
Step 3: With B as the centre, draw an arc of 3. 5 cm
. Name that point as A.
Step 4: With C as the centre, draw an arc of 4. 6 cm
. Name that point as D.
Step 5: Join A and D.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 1 0
Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ?Q = 45° and ?R = 90°.
S o l u t i o n :
Steps of construction:
Step 1: Draw QR= 5. 6 cm
Step 2: Make ?Q = 45
°
and ?R = 90
°
Step 3: With Q as the centre, draw an arc of 6 cm
. Name that point as P.
Step 4: With R as the centre, draw an arc of 2. 7cm
. Name that point as S.
Step 6: Join P and S.
Then, PQRS
is the required quadrilateral.
Q u e s t i o n : 1 1
Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ?A = 50°, ?B = 105° and ?D = 80°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 5. 6 cm
Step 2: Make ?A = 50
°
and ?B = 105
°
Step 3: With B as the centre, draw an arc of 4cm
.
Step 3: Sum of all the angles of the quadrilateral is 360
°
.
?A + ?B + ?C + ?D = 360
°
50
°
+105
°
+ ?C +80
°
= 360
°
235
°
+ ?C = 360
°
?C = 360
°
-235
°
?C = 125
°
Step 5: With C as the centre, make ?C equal to ?125
°
.
Step 6: Join C and D.
Step 7: Measure ?D = 80
°
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 1 2
Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ?P = ?R = 100° and ?S = 75°.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ= 5cm
Step 2:
?P + ?Q+ ?R + ?S = 360
°
100
°
+ ?Q+100
°
+75
°
= 360
°
275
°
+ ?Q = 360
°
?Q = 360
°
-275
°
?Q = 85
°
Step 3: Make ?P = 100
°
and ?Q = 85
°
Step 3: With Q as the centre, draw an arc of 6. 5 cm
.
Step 4: Make ?R = 100
°
Step 6: Join R and S.
Step 7: Measure ?S = 75
°
Then, PQRS
is the required quadrilateral.
Q u e s t i o n : 1 3
Page 5
Q u e s t i o n : 1
Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 4. 2 cm
.
Step 2: With A as the centre and radius equal to 8 cm
, draw an arc.
Step 3: With B as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to 5 cm,
draw an arc.
Step 6: With C as the centre and radius equal to 5. 2 cm
, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 2
Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ = 5. 4 cm
.
Step 2: With P as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With Q as the centre and radius equal to 4. 6 cm
, draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to 3. 5 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 4. 3 cm
, draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 3
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 5 cm
.
Step 2: With B as the centre and radius equal to 5. 6 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 4. 5 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to 4. 5 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 8 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 4
Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 6 cm
.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 2. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 4. 6 cm,
draw an arc.
Step 6: With B as the centre and radius equal to 3. 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 5
Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.
S o l u t i o n :
Steps of construction:
Step 1: Draw QR = 7. 5 cm.
Step 2: With Q as the centre and radius equal to 10 cm
, draw an arc.
Step 3: With R as the centre and radius equal to 5 cm
, draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to 6 cm,
draw an arc.
Step 6: With R as the centre and radius equal to 6 cm
, draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.
Q u e s t i o n : 6
construct a quadrilateral ABCD in which AB =3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 3. 4 cm.
Step 2: With B as the centre and radius equal to 4 cm
, draw an arc.
Step 3: With A as the centre and radius equal to 5. 7 cm
, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 8 cm,
draw an arc.
Step 6: With D as the centre and radius equal to 3 cm
, draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Q u e s t i o n : 7
Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ?ABC = 120°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 3. 5 cm
.
Step 2: Make ?ABC = 120
°
.
Step 3: With B as the centre, draw an arc 3. 5 cm
and name that point C.
Step 4: With C as the centre, draw an arc 5. 2 cm
.
Step 5: With A as the centre, draw another arc ?5. 2 cm
, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, ABCD
is the required quadrilateral.
Q u e s t i o n : 8
Construct a quadrilateral ABCD in which AB = 2.9 cm, BC = 3.2 cm, CD = 2.7 cm, DA = 3.4 cm and ?A = 70°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 2. 9cm
Step 2: Make ?A = 70
°
Step 3: With A as the centre, draw an arc of 3. 4cm
. Name that point as D.
Step 4: With D as the centre, draw an arc of 2. 7cm
.
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 9
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ?B = 125° and ?C = 60°.
S o l u t i o n :
Steps of construction:
Step 1: Draw BC= 5cm
Step 2: Make ?B = 125
°
and ?C = 60
°
Step 3: With B as the centre, draw an arc of 3. 5 cm
. Name that point as A.
Step 4: With C as the centre, draw an arc of 4. 6 cm
. Name that point as D.
Step 5: Join A and D.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 1 0
Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ?Q = 45° and ?R = 90°.
S o l u t i o n :
Steps of construction:
Step 1: Draw QR= 5. 6 cm
Step 2: Make ?Q = 45
°
and ?R = 90
°
Step 3: With Q as the centre, draw an arc of 6 cm
. Name that point as P.
Step 4: With R as the centre, draw an arc of 2. 7cm
. Name that point as S.
Step 6: Join P and S.
Then, PQRS
is the required quadrilateral.
Q u e s t i o n : 1 1
Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ?A = 50°, ?B = 105° and ?D = 80°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 5. 6 cm
Step 2: Make ?A = 50
°
and ?B = 105
°
Step 3: With B as the centre, draw an arc of 4cm
.
Step 3: Sum of all the angles of the quadrilateral is 360
°
.
?A + ?B + ?C + ?D = 360
°
50
°
+105
°
+ ?C +80
°
= 360
°
235
°
+ ?C = 360
°
?C = 360
°
-235
°
?C = 125
°
Step 5: With C as the centre, make ?C equal to ?125
°
.
Step 6: Join C and D.
Step 7: Measure ?D = 80
°
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 1 2
Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ?P = ?R = 100° and ?S = 75°.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ= 5cm
Step 2:
?P + ?Q+ ?R + ?S = 360
°
100
°
+ ?Q+100
°
+75
°
= 360
°
275
°
+ ?Q = 360
°
?Q = 360
°
-275
°
?Q = 85
°
Step 3: Make ?P = 100
°
and ?Q = 85
°
Step 3: With Q as the centre, draw an arc of 6. 5 cm
.
Step 4: Make ?R = 100
°
Step 6: Join R and S.
Step 7: Measure ?S = 75
°
Then, PQRS
is the required quadrilateral.
Q u e s t i o n : 1 3
Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ?ABC = ?ACD = 90°.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 4cm
Step 2: Make ?B = 90
°
Step 3: AC
2
= AB
2
+BC
2
5
2
= 4
2
+BC
2
25 -16 = BC
2
BC = 3cm
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make ?C = 90
°
Step 5: With A as the centre and radius equal to 5. 5 cm
, draw an arc and name that point as D.
Then, ABCD
is the required quadrilateral.
Q u e s t i o n : 1 4
Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB = 5. 2cm
Step 2: With B as the centre, draw an arc of 4. 7 cm
.
Step 3: With A as the centre, draw another arc of 7. 6 cm
, cutting the previous arc at C.
Step 4: Join A and C.
Step 5: We know that the opposite sides of a parallelogram are equal. Thus, with C as the centre, draw an arc of 5. 2cm
.
Step 6: With A as the centre, draw another arc of 4. 7 cm
, cutting the previous arc at D.
Step 7: Join CD and AD.
Then, ABCD is the required parallelogram.
Q u e s t i o n : 1 5
Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw AB= 4. 3cm
Step 2: With B as the centre, draw an arc of 6. 8 cm
.
Step 3: With A as the centre, draw another arc of 4cm
, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: We know that the opposite sides of a parallelogram are equal.
Thus, with D as the centre, draw an arc of 4. 3cm
.
Step 6: With B as the centre, draw another arc of 4 cm
, cutting the previous arc at C.
Step 7: Join CD and BC.
?then, ABCD is the required parallelogram.
Q u e s t i o n : 1 6
Construct a parallelogram PQRS in which QR = 6 cm, PQ = 4 cm and ?PQR = 60° cm.
S o l u t i o n :
Steps of construction:
Step 1: Draw PQ= 4 cm
Step 2: Make ?PQR = 60
°
Step 2: With Q as the centre, draw an arc of 6 cm and name that point as R.
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