Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 17 Construction Of Quadrilaterals are provided here with simple step-by-step explanations. These solutions for Construction Of Quadrilaterals are extremely popular among Class 8 students for Math Construction Of Quadrilaterals Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 17 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Page No 198:
Question 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.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With A as the centre and radius equal to , draw an arc.
Step 3: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to draw an arc.
Step 6: With C as the centre and radius equal to , draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 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.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With P as the centre and radius equal to , draw an arc.
Step 3: With Q as the centre and radius equal to , draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to draw an arc.
Step 6: With R as the centre and radius equal to , draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.
Thus, PQRS is the required quadrilateral.
Page No 198:
Question 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.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , 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 draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 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.
Answer:
Steps of construction:
Step 1: Draw .
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , 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 draw an arc.
Step 6: With B as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 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.
Answer:
Steps of construction:
Step 1: Draw
Step 2: With Q as the centre and radius equal to , draw an arc.
Step 3: With R as the centre and radius equal to , 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 draw an arc.
Step 6: With R as the centre and radius equal to , 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.
Page No 198:
Question 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.
Answer:
Steps of construction:
Step 1: Draw
Step 2: With B as the centre and radius equal to , draw an arc.
Step 3: With A as the centre and radius equal to , 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 draw an arc.
Step 6: With D as the centre and radius equal to , draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.
Thus, ABCD is the required quadrilateral.
Page No 198:
Question 7:
Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ∠ABC = 120°.
Answer:
Steps of construction:
Step 1: Draw AB= .
Step 2: Make .
Step 3: With B as the centre, draw an arc and name that point C.
Step 4: With C as the centre, draw an arc .
Step 5: With A as the centre, draw another arc , cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, is the required quadrilateral.
Page No 198:
Question 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°.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With A as the centre, draw an arc of . Name that point as D.
Step 4: With D as the centre, draw an arc of .
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, is the required quadrilateral.
Page No 198:
Question 9:
Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ∠B = 125° and ∠C = 60°.
Answer:
Steps of construction:
Step 1: Draw BC=
Step 2: Make
Step 3: With B as the centre, draw an arc of . Name that point as A.
Step 4: With C as the centre, draw an arc of . Name that point as D.
Step 5: Join A and D.
Then, is the required quadrilateral.
Page No 198:
Question 10:
Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ∠Q = 45° and ∠R = 90°.
Answer:
Steps of construction:
Step 1: Draw QR=
Step 2: Make
Step 3: With Q as the centre, draw an arc of . Name that point as P.
Step 4: With R as the centre, draw an arc of . Name that point as S.
Step 6: Join P and S.
Then, is the required quadrilateral.
Page No 198:
Question 11:
Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ∠A = 50°, ∠B = 105° and ∠D = 80°.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With B as the centre, draw an arc of .
Step 3: Sum of all the angles of the quadrilateral is .
Step 5: With C as the centre, make .
Step 6: Join C and D.
Step 7: Measure
Then, is the required quadrilateral.
Page No 199:
Question 12:
Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ∠P = ∠R = 100° and ∠S = 75°.
Answer:
Steps of construction:
Step 1: Draw PQ=
Step 2:
Step 3: Make
Step 3: With Q as the centre, draw an arc of .
Step 4: Make
Step 6: Join R and S.
Step 7: Measure
Then, is the required quadrilateral.
Page No 199:
Question 13:
Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90°.
Answer:
Steps of construction:
Step 1: Draw
Step 2:
Step 3:
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make
Step 5: With A as the centre and radius equal to , draw an arc and name that point as D.
Then, is the required quadrilateral.
Page No 201:
Question 1:
Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.
Answer:
Steps of construction:
Step 1: Draw AB =
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , 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 .
Step 6: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join CD and AD.
Then, ABCD is the required parallelogram.
Page No 201:
Question 2:
Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , 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 .
Step 6: With B as the centre, draw another arc of , cutting the previous arc at C.
Step 7: Join CD and BC.
then, ABCD is the required parallelogram.
Page No 201:
Question 3:
Construct a parallelogram PQRS in which QR = 6 cm, PQ = 4 cm and ∠PQR = 60° cm.
Answer:
Steps of construction:
Step 1: Draw PQ= 4 cm
Step 2: Make
Step 2: With Q as the centre, draw an arc of 6 cm and name that point as R.
Step 3: With R as the centre, draw an arc of 4 cm and name that point as S.
Step 4: Join SR and PS.
Then, PQRS is the required parallelogram.
Page No 201:
Question 4:
Construct a parallelogram ABCD in which BC = 5 cm, ∠BCD = 120° and CD = 4.8 cm.
Answer:
Steps of construction:
Step 1: Draw BC=
Step 2: Make an
Step 2: With C as centre draw an arc of , name that point as D
Step 3: With D as centre draw an arc , name that point as A
Step 4: With B as centre draw another arc cutting the previous arc at A.
Step 5: Join AD and AB
then, ABCD is a required parallelogram.
Page No 201:
Question 5:
Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm. Measure the other side.
Answer:
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AB=
Step 2: With A as the centre and radius , draw an arc.
Step 3: With B as the centre and radius , draw another arc, cutting the previous arc at point O.
Step 4: Join OA and OB.
Step 5: Produce OA to C, such that OC= AO. Produce OB to D, such that OB=OD.
Step 5: Join AD, BC, and CD.
Thus, ABCD is the required parallelogram. The other side is 4.5 cm in length.
Page No 201:
Question 6:
Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and the altitude AL from A is 2.5 cm. Draw the altitude from C and measure it.
Answer:
Steps of construction:
Step 1: Draw AB= 6.5cm
Step 2: Draw a perpendicular at point A. Name that ray as AX. From point A, draw an arc of length 2.5 cm on the ray AX and name that point as L.
Step 3: On point L, make a perpendicular. Draw a straight line YZ passing through L, which is perpendicular to the ray AX.
Step 4: Cut an arc of length 3.4 cm on the line YZ and name it as C.
Step 5: From point C, cut an arc of length 6.5 cm on the line YZ. Name that point as D.
Step 6: Join BC and AD.
Therefore, quadrilateral ABCD is a parallelogram.
The altitude from C measures 2.5 cm in length.
Page No 201:
Question 7:
Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.
Answer:
We know that the diagonals of a parallelogram bisect each other.
Steps of construction:
Step 1: Draw AC=
Step 2: Bisect AC at O.
Step 3: Make
Produce XO to Y.
Step 4:
Step 5: Join AB, BC, CD and AD.
Thus, ABCD is the required parallelogram.
Page No 201:
Question 8:
Construct a rectangle ABCD whose adjacent sides are 11 cm and 8.5 cm.
Answer:
Steps of construction:
Step 1: Draw AB =
Step 2: Make
Step 3: Draw an arc of 8.5 cm from point A and name that point as D.
Step 4: Draw an arc of 8.5 cm from point B and name that point as C.
Step 5: Join C and D.
Thus, ABCD is the required rectangle.
Page No 201:
Question 9:
Construct a square, each of whose sides measures 6.4 cm.
Answer:
All the sides of a square are equal.
Steps of construction:
Step 1: Draw AB =
Step 2: Make
Step 3: Draw an arc of length 6.4 cm from point A and name that point as D.
Step 4: Draw an arc of length 6.4 cm from point B and name that point as C.
Step 5: Join C and D.
Thus, ABCD is a required square.
Page No 201:
Question 10:
Construct a square, each of whose diagonals measures 5.8 cm.
Answer:
We know that the diagonals of a square bisect each other at right angles.
Steps of construction:
Step 1: Draw AC=
Step 2: Draw the perpendicular bisector XY of AC, meeting it at O.
Step 3:
:
Step 4: Join AB, BC, CD and DA.
ABCD is the required square.
Page No 201:
Question 11:
Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm. Measure the other side of the rectangle.
Answer:
Steps of construction:
Step 1: Draw QR =
Step 2: Make
Step 3:
Step 3: Draw an arc of length 4.8 cm from point Q and name that point as P.
Step 4: Draw an arc of length 6 cm from point R, cutting the previous arc at P.
Step 5: Join PQ
Step 6: Draw an arc of length 4.8 cm from point R.
From point P, draw an arc of length 3.6 cm, cutting the previous arc. Name that point as S.
Step 7: Join P and S.
Thus, PQRS is the required rectangle. The other side is 4.8 cm in length.
Page No 201:
Question 12:
Construct a rhombus the lengths of whose diagonals are 6 cm and 8 cm.
Answer:
We know that the diagonals of a rhombus bisect each other.
.Steps of construction:
Step 1: Draw AC=
Step 2:Draw a perpendicular bisector(XY) of AC, which bisects AC at O.
Step 3:
Draw an arc of length 4 cm on OX and name that point as B.
Draw an arc of length 4 cm on OY and name that point as D.
Step 4 : Join AB, BC, CD and AD.
Thus, ABCD is the required rhombus, as shown in the figure.
Page No 201:
Question 13:
Construct a rhombus ABCD in which AB = 4 cm and diagonal AC is 6.5 cm.
Answer:
Steps of construction:
Step 1: Draw AB =
Step 2: With B as the centre, draw an arc of .
Step 3: With A as the centre, draw another arc of , cutting the previous arc at C.
Step 4: Join AC and BC.
Step 5: With C as the centre, draw an arc of 4 cm.
Step 6: With A as the centre, draw another arc of , cutting the previous arc at D.
Step 7: Join AD and CD.
ABCD is the required rhombus.
Page No 201:
Question 14:
Draw a rhombus whose side is 7.2 cm and one angle is 60°.
Answer:
Steps of construction:
Step1: Draw AB =
Step2: Draw
Sum of the adjacent angles is 180°.
Step 3:
Step 4: Join C and D.
Then, ABCD is the required rhombus.
Page No 201:
Question 15:
Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75° and DC||AB.
Answer:
Steps of construction:
Step 1: Draw AB=
Step 2: Make
Step 3: With B as the centre, draw an arc at . Name that point as C.
Step 4:
Make
At C, draw an arc of length .
Step 5: Join A and D.
Thus, ABCD is the required trapezium.
Page No 201:
Question 16:
Draw a trapezium ABCD in which AB||DC, AB = 7 cm, BC = 5 cm, AD = 6.5 cm and ∠B = 60°.
Answer:
Steps of construction :
Step1: Draw AB equal to 7 cm.
Step2: Make an angle,
Step3: With B as the centre, draw an arc of . Name that point as C. Join B and C.
Step4:
Draw an angle,
Step4: With A as the centre, draw an arc of length , which cuts CY. Mark that point as D.
Step5: Join A and D.
Thus, ABCD is the required trapezium.
Page No 202:
Question 1:
Define the terms:
(i) Open curve
(ii) Closed curve
(iii) Simple closed curve
Answer:
( i) Open curve: An open curve is a curve where the beginning and end points are different.
Example: Parabola
(ii) Closed Curve: A curve that joins up so there are no end points.
Example: Ellipse
(iii) Simple closed curve: A closed curve that does not intersect itself.
Page No 202:
Question 2:
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find the measure of each angle.
Answer:
Let the angles be
Sum of the angles of a quadrilateral is .
The angles of the quadrilateral are
Page No 202:
Question 3:
Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find the measure of each of its angles.
Answer:
Sum of any two adjacent angles of a parallelogram is .
Measures of the angles are .
Page No 202:
Question 4:
The sides of a rectangle are in the ratio 4 : 5 and its perimeter is 180 cm. Find its sides.
Answer:
Let the length be cm and the breadth be cm.
Perimeter of the rectangle =180
Perimeter of the rectangle=
Page No 202:
Question 5:
Prove that the diagonals of a rhombus bisect each other at right angles.
Answer:
Rhombus is a parallelogram.
Therefore, the diagonals bisects at O.
Now, let us prove that the diagonals intersect each other at right angles.
Consider :
∴
∴ (corresponding parts of congruent triangles)
Further,
∴
It is proved that the diagonals of a rhombus are perpendicular bisectors of each other.
Page No 202:
Question 6:
The diagonals of a rhombus are 16 cm and 12 cm. Find the length of each side of the rhombus.
Answer:
All the sides of a rhombus are equal in length.
The diagonals of a rhombus intersect at .
The diagonal and the side of a rhombus form right triangles.
In :
Therefore, the length of each side of the rhombus is 10 cm.
Page No 202:
Question 7:
Mark (✓) against the correct answer:
Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. The measures of all its angles are
(a) 97°, 83°, 97°, 83°
(b) 37°, 143°, 37°, 143°
(c) 76°, 104°, 76°, 104°
(d) none of these
Answer:
(b) 37o, 143o, 37o 143o
Opposite angles of a parallelogram are equal.
Therefore, the first and the second angles are:
Sum of adjacent angles in a parallelogram is .
Adjacent angles =
Page No 202:
Question 8:
Mark (✓) against the correct answer:
The angles of quadrilateral are in the ratio 1 : 3 : 7 : 9. The measure of the largest angle is
(a) 63°
(b) 72°
(c) 81°
(d) none of these
Answer:
(d) none of the these
Let the angles be .
Sum of the angles of the quadrilateral is .
Page No 202:
Question 9:
Mark (✓) against the correct answer:
The length of a rectangle is 8 cm and each of its diagonals measures 10 cm. The breadth of the rectangle is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 9 cm
Answer:
(b) 6 cm
Let the breadth of the rectangle be x cm.
Diagonal =10 cm
Length= 8 cm
The rectangle is divided into two right triangles.
Breadth of the rectangle = 6 cm
Page No 202:
Question 10:
Mark (✓) against the correct answer:
In a square PQRS, if PQ = (2x + 3) cm and QR = (3x − 5) cm then
(a) x = 4
(b) x = 5
(c) x = 6
(d) x = 8
Answer:
(d) x = 8
All sides of a square are equal.
Page No 202:
Question 11:
Mark (✓) against the correct answer:
The bisectors of two adjacent angles of a parallelogram intersect at
(a) 30°
(b) 45°
(c) 60°
(d) 90°
Answer:
(d) 90°
We know that the opposite sides and the angles in a parallelogram are equal.
Also, its adjacent sides are supplementary, i.e. sum of the sides is equal to 180.
Now, the bisectors of these angles form a triangle, whose two angles are:
Hence, the two bisectors intersect at right angles.
Page No 202:
Question 12:
Mark (✓) against the correct answer:
How many diagonals are there in a hexagon?
(a) 6
(b) 8
(c) 9
(d) 10
Answer:
(c) 9
Hexagon has six sides.
Page No 202:
Question 13:
Mark (✓) against the correct answer:
Each interior angle of a polygon is 135. How many sides does it have?
(a) 10
(b) 8
(c) 6
(d) 5
Answer:
(b) 8
It has 8 sides.
Page No 202:
Question 14:
Fill in the blanks.
For a convex polygon of n sides, we have:
(i) Sum of all exterior angles = .........
(ii) Sum of all interior angles = .........
(iii) Number of diagonals = .........
Answer:
(i) Sum of all exterior angles =
(ii) Sum of all interior angles =
(iii) Number of diagonals =
Page No 202:
Question 15:
Fill in the blanks.
For a regular polygon of n sides, we have:
(i) Sum of all exterior angles = .........
(ii) Sum of all interior angles = .........
Answer:
(i) Sum of all exterior angles of a regular polygon is .
(ii) Sum of all interior angles of a polygon is
Page No 202:
Question 16:
Fill in the blanks.
(i) Each interior angle of a regular octagon is (.........)°.
(ii) The sum of all interior angles of a regular hexagon is (.........)°.
(iii) Each exterior angle of a regular polygon is 60°. This polygon is a .........
(iv) Each interior angle of a regular polygon is 108°. This polygon is a .........
(v) A pentagon has ......... diagonals.
Answer:
(i) Octagon has 8 sides.
(ii) Sum of the interior angles of a regular hexagon =
(iii) Each exterior angle of a regular polygon is .
Therefore, the given polygon is a hexagon.
(iv) If the interior angle is , then the exterior angle will be . (interior and exterior angles are supplementary)
Sum of the exterior angles of a polygon is 360°.
Let there be n sides of a polygon.
Since it has 5 sides, the polygon is a pentagon.
(v) A pentagon has 5 diagonals.
Page No 203:
Question 17:
Write 'T' for true and 'F' for false for each of the following:
(i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rectangle are perpendicular to each other.
(iii) The diagonals of a rhombus bisect each other at right angles.
(iv) Every rhombus is a kite.
Answer:
(i) F
The diagonals of a parallelogram need not be equal in length.
(ii) F
The diagonals of a rectangle are not perpendicular to each other.
(iii) T
(iv) T
Adjacent sides of a kite are equal and this is also true for a rhombus. Additionally, all the sides of a rhombus are equal to each other.
Page No 203:
Question 18:
Construct a quadrilateral PQRS in which PQ = 4.2 cm, ∠PQR = 60°, ∠QPS = 120°, QR = 5 cm and PS = 6 cm.
Answer:
Steps of construction:
Step 1: Take PQ = 4.2 cm
Step 2:
Step 3: Cut an arc of length 5 cm from point Q. Name that point as R.
Step 4: From P, make an arc of length 6 cm. Name that point as S.
Step 5: Join P and S.
Thus, PQRS is a quadrilateral.
View NCERT Solutions for all chapters of Class 8