Category: ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 16 Symmetry Reflection and Rotation

Question 1.
Draw the line or lines of symmetry, if any, of the following shapes and count their number:

Solution:

Question 2.
For each of the given shape in question 1, find the order of the rotational symmetry (if any).
Solution:

Question 3.
Construct a rectangle ABCD such that AB = 4.5 cm and BC = 3 cm. Draw its line (or lines) of symmetry.
Solution:

Question 4.
Construct a rhombus ABCD with AB = 5.3 cm and ∠A = 60°. Draw its line (or lines) of symmetry.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 15 Circle Check Your Progress

Question 1.
Draw a circle of radius 2·7 cm. Draw a chord PQ of length 4 cm of this circle. Shade the major segment of this circle.
Solution:

Question 2.
Draw a circle of radius 3·2 cm and in it make a sector of angle.
(i) 30°
(ii) 135°
(iii) \(2 \frac{2}{3}\) right angles
Draw separate diagrams and shade the sectors.
Solution:

Question 3.
Draw a line segment PQ = 6·4 cm. Construct a circle on PQ as diameter. Take any point R on this circle and measure ∠PRQ.
Solution:

Question 4.
In the adjoining figure, the tangent to a circle of radius 6 cm from an external point P is of length 8 cm. Calculate the distance of the point P from the nearest point of the circumference.

Solution:

Question 5.
In the given figure, O is the centre of the circle. If ∠ABP = 35° and ∠BAQ = 65°, find
(i) ∠PAB
(ii) ∠QBA

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 15 Circle Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) A chord of a circle is a line segment with its endpoints ……………
(ii) A diameter of a circle is a chord that …………… the centre of the circle.
(iii) A line meets a circle almost in …………… points.
(iv) One-half of the whole arc of a circle is called a …………… of the circle.
(v) The angle subtended by an arc of a circle at the centre of the circle is called the …………… by the arc.
(vi) A line which meets a circle in one and only one point is called a …………… to the circle.
(vii) The tangent at any point of a circle and the radius through that point are …………… to each other.
(viii) From a point outside the circle, …………… tangents can be drawn to the circle.
(ix) The measure of an angle in a semicircle is ……………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) A line segment with its end-points lying on a circle is called a radius of the circle.
(ii) Diameter is the longest chord of the circle.
(iii) The end-points of a diameter of a circle divide the circle into two parts; each part is called a semicircle.
(iv) A diameter of a circle divides the circular region into two parts; each part is called a semicircular region.
(v) The diameters of a circle are concurrent. The centre of the circle is the point common to all diameters.
(vi) Every circle has unique centre and it lies inside the circle.
(vii) Every circle has unique diameter.
(viii) From a given point in the exterior of a circle, two tangents can be drawn to it and these two tangents are equal in length.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 6):
Question 3.
If P and Q are any two points on a circle, then the line segment PQ is called a
(a) radius of the circle
(b) diameter of the circle
(c) chord of the circle
(d) secant of the circle
Solution:

Question 4.
If P is a point in the interior of a circle with centre O and radius r, then
(a) OP = r
(b) OP > r
(c) OP > r
(d) OP < r
Solution:

Question 5.
If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is
(a) 6 cm
(b) 8 cm
(c) 10 cm
(d) 20 cm
Solution:

Question 6.
In the given figure, AB is a diameter of the circle. If AC = BC, then ∠CAB is equal to
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 15 Circle

Question 1.
Draw a circle with centre O and radius 2.5 cm. Draw two radii OA and OB such that ∠ AOB = 60°. Measure the length of the chord AB.
Solution:

Question 2.
Draw a circle of radius 3·2 cm. Draw a chord AB of this circle such that AB = 5 cm. Shade the minor segment of the circle.
Solution:

Question 3.
Find the length of the tangent drawn to a circle of radius 3 cm, from a point at a distance 5 cm from the centre.
Solution:

Question 4.
In the adjoining figure, PT is a tangent to the circle with centre C. Given CP = 20 cm and PT = 16 cm, find the radius of the circle.

Solution:

Question 5.
In each of the following figure, O is the centre of the circle. Find the size of each lettered angle :

Solution:

Question 6.
In each of the following figures, O is the j centre of the circle. Find the values of x and y.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Check Your Progress

Question 1.
Construct a quadrilateral ABCD such that AB = 4·5 cm, BC = 4 cm, CD = 3·9 cm, AD = 3·2 cm and ∠B = 60°.
Solution:

Question 2.
Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4·2 cm, AD = 3·5 cm, ∠A = 90°, ∠B = 60°.
Solution:

Question 3.
Construct a quadrilateral ABCD in which AB 3·5 cm, BC = 5 cm, CD = 5·6 cm, DA = 4 cm and BD = 5·4 cm
Solution:

Question 4.
Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2·5 cm, PS = 3·5 cm, PR = 4 cm and QS = 5 cm.
Solution:

Question 5.
Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.
Solution:

Question 6.
Construct a parallelogram ABCD in which AB = 5.2 cm, AC = 6.5 cm and BD = 7.8 cm.
Solution:

Question 7.
Construct a parallelogram ABCD in which diagonal AC = 4 cm, diagonal BD = 6 cm and angle between diagonals is 75°.
Solution:

Question 8.
Construct a rectangle PQRS such that PQ = 3·5 cm and ∠RPS = 75°.
Solution:

Question 9.
Construct a rectangle whose one diagonal is 6-8 cm and an angle between two diagonals is 105°.
Solution:

Question 10.
Construct a rhombus BEST such that BE = 4.5 cm, ET = 6 cm.
Solution:

Question 11.
Construct a rhombus whose diagonals are 7 cm and 5·3 cm.
Solution:

Question 12.
Construct a square whose one diagonal is 5·8 cm.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Objective Type Questions

Higher Order Thinking Skills (Hots)
Question 1.
Construct a trapezium ABCD in which AB = 7 cm, BC = 4 cm, CD = 3 cm, ∠B = 60° and AB || DC.
Solution:

Question 2.
Construct a parallelogram PQRS in which PQ = 6 cm, ∠Q = 120° and ∠RPQ = 30°.
Solution:

Question 3.
Construct a rectangle ABCD in which diagonal AC = 7 cm and the diagonals BD and AC intersect at O such that ∠BOC = 45°.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.2

Question 1.
Construct a parallelogram ABCD such that AB = 5 cm, BC = 3·2 cm and ∠B 120°.
Solution:

Question 2.
Construct a parallelogram ABCD such that AB = 4·8 cm, BC = 4 cm and diagonal BD = 5·4 cm.
Solution:

Question 3.
Construct a parallelogram ABCD such that BC = 4·5 cm, BD = 4 cm and AC = 5·6 cm.
Solution:

Question 4.
Construct a parallelogram ABCD such that AC = 6 cm, BD = 4·6 cm and angle between them is 45°.
Solution:

Question 5.
Construct a rectangle whose adjacent sides are 5·6 cm and 4 cm.
Solution:

Question 6.
Construct a rectangle such that one side is 5 cm and one diagonal is 6·8 cm.
Solution:

Question 7.
Construct a rectangle ABCD such that AB = 4 cm and ∠BAC = 60°.
Solution:

Question 8.
Construct a rectangle such that one diagonal is 6-6 cm and the angle between two diagonals is 120°.
Solution:

Question 9.
Construct a rhombus whose one side is 5 cm and one angle is 45°
Solution:

Question 10.
Construct a rhombus whose one side is 4·5 cm and one diagonal is 5 cm.
Solution:

Question 11.
Construct a rhombus whose diagonals are 6·8 cm and 5·2 cm.
Solution:

Question 12.
Construct a square whose one side is 4·3 cm.
Solution:

Question 13.
Construct a square whose one diagonal is 6·2 cm.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 14 Constructions of Quadrilaterals Ex 14.1

Question 1.
Construct a quadrilateral PQRS where PQ = 4.5 cm, QR = 6 cm, RS = 5.5 cm, PS = 5 cm and PR = 6.5 cm.
Solution:

Question 2.
Construct a quadrilateral ABCD in which AB = 3·5 cm, BC = 5 cm, CD = 5·6 cm, DA = 4 cm and BD = 5·4 cm
Solution:

Question 3.
Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2·5 cm, PS = 3·5 cm, PR = 4 cm and QS = 5 cm.
Solution:

Question 4.
Construct a quadrilateral ABCD such that BC = 5 cm, AD = 5.5 cm, CD = 4.5 cm, AC = 7 cm, and BC = 5.5 cm.
Solution:

Question 5.
Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.
Solution:

Question 6.
Construct a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, ∠P = 60°, ∠Q = 90° and ∠R = 120°.
Solution:

Question 7.
Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4·2 cm, AD = 3·5 cm, ∠A = 90°, and ∠B = 60°
Solution:

Question 8.
Cosntruct a quadrilateral PQRS where PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, ∠Q = 60° and ∠R = 90°.
Solution:

Question 9.
Construct a quadrilateral BEST where BE = 3.8 cm, ES = 3.4 cm, ST = 4.5 cm, TB = 5 cm and ∠E = 80°.
Solution:

Question 10.
Construct a quadrilateral ABCD where AB = 4·5 cm, BC = 4 cm, CD = 3·9 cm, AD = 3·2 cm and ∠B = 60°.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 13 Understanding Quadrilaterals Check Your Progress

Question 1.
From the given diagram, find the value of x.

Solution:

Question 2.
If two angles of a quadrilateral are 77° and 51°, and out of the remaining two angles, one angle is 10° smaller than the other, find these angles.
Solution:

Question 3.
In the given figure, AB || DC, ∠A = 74° and ∠B : ∠C = 4 : 5. Find
(i) ∠D
(ii) ∠B
(iii) ∠C

Solution:

Question 4.
In quadrilateral ABCD, ∠A : ∠B : ∠C : ∠D = 3 : 4 : 6 : 7. Find all the angles of the quadrilateral. Hence, prove that AB and DC are parallel. Is BC also parallel to AD?
Solution:

Question 5.
One angle of a parallelogram is two-third of the other. Find the angles of the parallelogram.
Solution:

Question 6.
In the given figure, ABCD is a kite. If ∠BCD = 52° and ∠ADB = 42°, find the values of x, y, and z.

Solution:

Question 7.
In the given figure, ABCD is a rectangle. Prove that AC = BD.

Solution:

Question 8.
In the given figure, ABCD is a rhombus and EDC is an equilateral triangle. If ∠DAB = 48°, find
(i) ∠BEC
(ii) ∠DEB
(iii) ∠BFC

Solution:

Question 9.
Find the number of sides of a regular polygon if each of its interior angles is 168°.
Solution:

Question 10.
If the sum of interior angles of a polygon is 3780° find the number of sides.
Solution:

Question 11.
The angles of a hexagon are (2x + 5)°, (3x – 5)°, (x + 40)°, (2x + 20)°, (2x + 25)° and (2x + 35)°. Find the value of x.
Solution:

Question 12.
Two angles of a polygon are right angles and every other angle is 120°. Find the number of sides of the polygon.
Solution:

Question 13.
The sum of interior angles of a regular polygon is twice the sum of its exterior angles. Find the number of sides of the polygon.
Solution:

Question 14.
An exterior angle of a regular polygon is one- fourth of its interior angle. Find the number of sides in the polygon.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 13 Understanding Quadrilaterals Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The curves which have different beginning and endpoints are called …………
(ii) A curve which does not cross itself at any point is called a …………
(iii) A simple closed curve made up entirely of line segments is called a …………
(iv) A polygon in which each interior angle is less than 180° is called a …………
(v) 10 sided polygon is called …..
(vi) A polygon which has all its sides of equal length and all its angles of equal measure is called a …………
(vii) Sum of all exterior angles of a polygon is …………
(vi) A polygon which has all its sides of equal length and all its angles of equal measure is called a …………
(vii) Sum of all exterior angles of a polygon is …………
(viii) Sum of all interior angles of a n-sided polygon is …………
(ix) The adjacent angles of a parallelogram are …………
(x) If an angle of a parallelogram is a right angle, then it is called a …………
(xi) If two adjacent sides of a parallelogram are equal, then it is called a …………
(xii) It two adjacent sides of a rectangle are equal, then it is called a …………
(xiii) The diagonal of a rhombus bisect each other at …………
(xiv) A quadrilateral in which one pair of opposite sides is parallel is called a …………
(xv) A quadrilateral in which two pairs of adjacent sides are equal is called a …………
(xvi) If two non-parallel sides of a trapezium are equal then it is called …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) The curves which have the same beginning and endpoints are called open curves.
(ii) The region of the plane that lies inside the curve is called the interior of the curve.
(iii) A polygon in which at least one interior angle is greater than 180° is called convex polygon.
(iv) 6 sided polygon is called hexagon.
(v) Sum of all interior angles of a quadrilateral is 180°.
(vi) Each interior angle of a n-sided regular polygon is \(\frac{(2 n-4) \times 90^{\circ}}{n}\).
(vii) The diagonals of a parallelogram bisect each other at right angles.
(viii) The opposite angles of a parallelogram are of equal measure.
(ix) The diagonals of a rhombus bisect the angles of a rhombus.
(x) The diagonals of a square are not equal.
(xi) Co-interior angles of a parallelogram are supplementary.
(xii) The diagonals of a kite bisect at right angles.
(xiii) All rectangles are squares.
(xiv) All rhombuses are parallelograms.
(xv) All squares are rhombuses and also rectangles.
(xvi) All squares are not parallelograms.
(xvii) All kites are rhombuses.
(xviii) All rhombuses are kites.
(xix) All parallelograms are trapeziums.
(xx) All squares are trapeziums.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 19):
Question 3.
Sum of all interior angles of an 11-sided polygon is
(a) 1620°
(b) 1440°
(c) 1260v
(d) none of these
Solution:

Question 4.
If each interior angle of a regular polygon is 144°, then number of sides of polygon is
(a) 8
(b) 9
(c) 10
(d) 11
Solution:

Question 5.
If the sum of all interior angles of a polygon is 1260°, then number of sides of polygon is
(a) 6
(b) 7
(c) 8
(d) 9
Solution:

Question 6.
The sum of all exterior angles of a pentagon is
(a) 590°
(b) 360°
(c) 180°
(d) none of these
Solution:

Question 7.
If the ratio between an exterior and interior angle of a regular polygon is 1 : 5, then the number of sides of the polygon is
(a) 11
(b) 12
(c) 13
(d) 14
Solution:

Question 8.
In the given figure, the value of x is
(a) 140°
(b) 50°
(c) 130°
(d) 40°

Solution:

Question 9.
In the given figure, the value of x is
(a) 120°
(b) 130°
(c) 140°
(d) 150°

Solution:

Question 10.
In the given figure, the value of x + y + z + w is
(a) 180°
(b) 270°
(c) 300°
(d) 360°

Solution:

Question 11.
In the given figure, the value of x + y is
(a) 180°
(b) 190°
(c) 170°
(d) 160°

Solution:

Question 12.
The lengths of two adjacent sides of a parallelogram are in the ratio 1 : 2. If the perimeter of a parallelogram is 60 cm, then the length of its sides are
(a) 6 cm, 12 cm
(b) 8 cm, 16 cm
(c) 9 cm, 18 cm
(d) 10 cm, 20 cm
Solution:

Question 13.
In the given figure, ABCD is a parallelogram, the values of x and y respectively are
(a) 1 cm, 1 cm
(b) 2 cm, 1 cm
(c) 1 cm, 2 cm
(d) 2 cm, 2 cm

Solution:

Question 14.
In the given figure, ABCD is a parallelogram, the values of x, y and z respectively are
(a) 60°, 60°, 70°
(b) 60°, 70°, 60°
(c) 70°, 60°, 60°
(d) none of these

Solution:

Question 15.
In the given figure, ABCD is a rectangle, the value of angle x is
(a) 60°
(b) 90°
(c) 120°
(d) none of these

Solution:

Question 16.
In a rhombus ABCD, the diagonals AC and BD are respectively 8 cm and 6 cm. The length of each side of the rhombus is
(a) 7 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm
Solution:

Question 17.
In the given figure, ABCD is a square, the value of angle x is
(a) 30°
(b) 45°
(c) 60°
(d) not possible to find

Solution:

Question 18.
In the given figure, ABCD is a kite, the value of angle x is
(a) 86°
(b) 100°
(c) 104°
(d) none of these

Solution:

Question 19.
In the given figure, ABCD is an isosceles trapezium. The values of x, y and z respectively are
(a) 110°, 110°, 70°
(b) 110°, 70°, 110°
(c) 70°, 110°, 110°
(d) none of these

Solution:

Higher Order Thinking Skills (Hots)
Question 1.
In the given figure, ABCDEF is a regular hexagon. Prove that quadrilaterals ABDE and ACDF are parallelograms. Also prove that quadrilateral AGDH is a parallelogram.

Solution:

Question 2.
In the given figure, ABCD is a parallelogram and M, N are the mid-points of sides BC, AD respectively. Prove that EA = AB = BF.

Solution:

Question 3.
Prove that the quadrilateral formed by joining the mid-points of the adjacent sides of a rectangle is a parallelogram.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 13 Understanding Quadrilaterals Ex 13.3

Question 1.
Identify all the quadrilaterals that have
(i) four sides of equal length
(ii) four right angles.
Solution:

Question 2.
Explain how a square is
(i) a quadrilateral
(ii) a parallelogram
(iii) a rhombus
(iv) a rectangle.
Solution:

Question 3.
Name the quadrilaterals whose diagonals
(i) bisect each other
(ii) are perpendicular bisectors of each other
(iii) are equal.
Solution:

Question 4.
One of the diagonals of a rhombus and its sides are equal. Find the angles of the rhombus.
Solution:

Question 5.
In the given figure, ABCD is a rhombus, find the values of x, y and z.

Solution:

Question 6.
In the given figure, ABCD is a trapezium. If ∠A : ∠D = 5 : 7, ∠B = (3x + 11)° and ZC = (5x – 31)°, then find all the angles of the trapezium.

Solution:

Question 7.
In the given figure, ABCD is a rectangle. If ∠CEB : ∠ECB = 3 : 2 find
(i) ∠CEB,
(ii) ∠DCF

Solution:

Question 8.
In the given figure, ABCD is a rectangle and diagonals intersect at O. If ∠AOB = 118°, find

(i) ∠ABO
(ii) ∠ADO
(iii) ∠OCB
Solution:

Question 9.
In the given figure, ABCD is a rhombus and ∠ABD = 50°. Find :
(i) ∠CAB
(ii) ∠BCD
(iii) ∠ADC

Solution:

Question 10.
In the given isosceles trapezium ABCD, ∠C = 102°. Find all the remaining angles of the trapezium.

Solution:

Question 11.
In the given figure, PQRS is a kite. Find the values of x and y.

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths