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 ....
Answer
(i) A figure has line symmetry if it is its own image under a reflection.
(ii) A kite has one line(s) of symmetry.
(iii) A parallelogram has no line(s) of symmetry.
(iv) The centre of rotation of an equilateral triangle is the point of intersection of its angle bisectors/medians/altitudes.
(v) The centre of rotation of a rhombus is the point of intersection of its diagonals.
(vi) A regular polygon of -sides has number of lines of symmetry.
(vii) Angle of rotational symmetry in an equilateral triangle is 120°.
(viii) Angle of rotational symmetry in a regular pentagon is 72°.
(ix) If after a rotation of 45° about a fixed point the figure looks exactly the same, then the order of rotational symmetry is 8.
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
(iii) 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.
Answer
(i) False
Reason:
A parallelogram has no line of symmetry. Each diagonal divides it into two congruent triangles, but on folding the parallelogram about a diagonal the two parts do not coincide.
(ii) False
Reason:
A regular triangle is an equilateral triangle. It has three lines of symmetry, which are the bisectors of its angles, and rotational symmetry of order 3, but it has no point of symmetry.
(iii) True
Reason:
A regular quadrilateral is a square. It has four lines of symmetry, which are the lines joining the mid-points of its opposite sides and its diagonals, one point of symmetry, which is the point of intersection of its diagonals, and rotational symmetry of order 4.
(iv) False
Reason:
A parallelogram looks exactly the same on being rotated through 180° about the point of intersection of its diagonals. So, it has rotational symmetry of order 2.
(v) False
Reason:
A regular pentagon has no point of symmetry, as on rotating it through 180° about its centre it does not look the same as in its starting position.
(vi) False
Reason:
The letter Z has no line of symmetry. It has one point of symmetry and rotational symmetry of order 2.