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.
Write the letters of the word ‘NEW ALGEBRA’ which have no line of symmetry.
Solution:
Mental Maths
Question 1.
Fill in the blanks:
(i) A figure has ………….. symmetry if it is its own image under a reflection.
(ii) A kite has ………….. line(s) of symmetry.
(iii) A parallelogram has ………….. line(s) of symmetry.
(iv) The centre of rotation of an equilateral triangle is the point of intersection of its …………..
(v) The centre of rotation of a rhombus is the point …………..
(vi) A regular polygon of n-sides has ………….. number of lines of symmetry.
(vii) Angle of rotational symmetry in an equilateral triangle is …………..
(viii) Angle of rotational symmetry in a regular pentagon is …………..
(ix) If after a rotation of 45° about a fixed point the figure looks exactly the same, then the order of rotational symmetry is …………..
Solution:
Question 2.
State whether the following statements are true (T) or false (F):
(i) A parallelogram has diagonals as its lines of symmetry.
(ii) A regular triangle has three lines of symmetry, one point of symmetry and has rotational symmetry of order 3.
(iiii) A, regular quadrilateral has four lines of symmetry, one point of symmetry and has . rotational symmetry of order 4.
(iv) A parallelogram has no rotational symmetry.
(v) A regular pentagon has one point of symmetry.
(vi) The letter Z has one line of symmetry.
Solution:
Multiple Choice Questions
Choose the correct answer from the given four options (3 to 6):
Question 3.
The number of lines of symmetry which a quadrilateral cannot have
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
Question 4.
A possible angle of rotation of a figure having rotational symmetry of order greater than or equal to 2 is
(a) 36°
(b) 144°
(c) 150°
(d) 360°
Solution:
Question 5.
The figure which does not have both line and rotational symmetry is
Solution:
Question 6.
The letter which has both line and rotational symmetry is
Solution:
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:
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:
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:
