Exercise 18A
Page-216Question 1:
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A scalene triangle has
(a) no line of symmetry
(b) one line of symmetry
(c) two lines of symmetry
(d) three lines of symmetry
Answer 1:
(a) no line of symmetry
Question 2:
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A rectangle is symmetrical about
(a) each one of its sides
(b) each one of its diagonals
(c) a line joining the midpoints of its opposite sides
(d) none of these
Answer 2:
(c) a line joining the midpoints of its opposite sides
Question 3:
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A square has
(a) one line of symmetry
(b) two lines of symmetry
(c) three lines of symmetry
(d) four lines of symmetry
Answer 3:
(d) four lines of symmetry
A square is symmetrical about both of its diagonals and both lines joining the midpoints of its opposite sides.
Question 4:
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A rhombus is symmetrical about
(a) the line joining the midpoints of its opposite sides
(b) each of its diagonals
(c) perpendicular bisector of each of its sides
(d) none of these
Answer 4:
(b) each of its diagonal
Question 5:
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A circle has
(a) no line of symmetry
(b) one line of symmetry
(c) two lines of symmetry
(d) an unlimited number of lines of symmetry
Answer 5:
(d) an unlimited number of lines of symmetry
A circle is symmetrical about all its diameters and a circle has unlimited number of diameters.
Therefore, a circle has unlimited number of lines of symmetry.
Question 6:
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In ∆ABC, AB = AC and AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Then ∆ABC is symmetrical about
(a) AD
(b) BE
(c) CF
(d) none of these
Answer 6:
(a) AD
This triangle is symmetrical only about AD.
Any isosceles triangle is symmetrical about its one altitude, which is drawn from the vertex between the two equal sides to the unequal side of the triangle.
Question 7:
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ABCD is a kite in which AB = AD and BC = DC. The kite is symmetrical about
(a) the diagonal AC
(b) the diagonal BD
(c) none of these
Answer 7:
(a) the diagonal AC
Since the part ABC is symmetrical to the part ADC, AC divides the figure into two equal parts.
Question 8:
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The letter O of the English alphabet has
(a) no line of symmetry
(b) one line of symmetry
(c) two lines of symmetry
(d) none of these
Answer 8:
(c) two lines of symmetry
The letter O of the English alphabetic system is symmetrical about its horizontal and vertical line.
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Question 9:
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the letter Z of the English alphabet has
(a) no line of symmetry
(b) one line of symmetry
(c) two lines of symmetry
(d) none of these
Answer 9:
(a) no line of symmetry
Question 10:
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Draw the line (or lines) of symmetry of each of the following figures.
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Answer 10:
Lines of symmetry are shown by the dotted lines.
(i)
(ii)
(iii)
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(iv)
Question 11:
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Which of the following statements are true and which of them are false?
(i) A parallelogram has no line of symmetry.
(ii) An angle with equal arms has its bisector as the line of symmetry.
(iii) An equilateral triangle has three lines of symmetry.
(iv) A rhombus has four lines of symmetry.
(v) A square has four lines of symmetry.
(vi) A rectangle has two lines of symmetry.
(vii) Each one of the letters H, I, O, X of the English alphabet has two lines of symmetry.
Answer 11:
(i) True
(ii) True
(iii) True
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(iv) False
A rhombus is symmetrical about both of its diagonals.
So, a rhombus has two lines of symmetry.
(v) True
A square is symmetrical about both of its diagonals and both the lines joining the midpoints of its opposite sides.
So, a square has four lines of symmetry.
(vi) True
A rectangle is symmetrical about both the lines joining the midpoints of its opposite sides.
So, a rectangle has two lines of symmetry.
(vii) True
Each one of the letters, H, I, O and X, of the English alphabetic system is symmetrical about its horizontal and vertical line, in the middle of the letters.
So, all these letters have two lines of symmetry.
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