12/27/2023 0 Comments Lines of symmetry in a rectangleLinear Symmetry: Two lines of symmetry each of which is a line joining the mid-points of two opposite sides of the rectangle. Rotational Symmetry: Possesses a rotational symmetry of order 2 about the point of intersection ‘O’ of its diagonals. Point of Symmetry: Possesses a point symmetry with the point of intersection ‘O’ of its diagonals as the centre of symmetry. Linear Symmetry: Two lines of symmetry i.e., its two diagonals Rotational Symmetry: Possesses a rotational symmetry of order 4 about the point of intersection ‘O’ of its diagonals. Point Symmetry: Possesses a point symmetry with the point of intersection ‘O’ of its diagonals as the centre of symmetry. Linear Symmetry: Four lines of symmetry i.e., its two diagonals and the two lines each joining the midpoint of the opposite sides of the square. Linear Symmetry: One line of symmetry i.e., the bisector PQ of the angle included between equal sides. Rotational Symmetry: Possesses a rotational symmetry of order 3 about the point of intersection ‘O’ of the bisector of the interior angles. the bisector of the three interior angles. Linear Symmetry: Three lines of symmetry i.e. Rotational Symmetry: No rotational symmetry Linear Symmetry: One line of symmetry i.e., the bisector PQ of the angle. Rotational Symmetry: Possesses a rotational symmetry of order 2 about the mid-point ‘O’ of the line segment. Point Symmetry: Possesses a point symmetry having the midpoint ‘O’ of the line segment as the center of symmetry. Linear Symmetry: One line of symmetry i.e., the perpendicular bisector PQ of the line segment. THREE TYPES OF SYMMETRIES FOR VARIOUS GEOMETRICAL FIGURES 1) possesses a rotational symmetry of order 3.Ĥ. If an equilateral triangle ABC is rotated through 360 0 about the point ‘O’ (point of intersection of angle bisectors), it attains the original form three time (upon rotation through 120 ∘, 240 ∘ and 360 ∘) as shown below:Ĭlearly, the above figure (Fig. 1) possesses rotational symmetry of order 2. Thus, the order of rotational symmetry of a figure may be defined as the number of times the figure fits onto itself in the process of rotational through 360 0.Įg: While rotating the following figure through 360 0 about the point ‘O’(mid-point of BC), it attains the original form twice (upon rotating through 180 0 and 360 0) as shown below:Ĭlearly, the above figure (fig. If A 0 is the smallest angle by which a particular figure has to be rotated so that its rotated from fits onto the original form, then the order of rotational symmetry is given by 360 0 A.įor a figure to possess a rotational symmetry, we must have A ∘ ≤ 180 ∘. Also the figure retains its original shape when rotated through 180 0.Ī figure is said to possess a rotational symmetry if it fits onto itself more than once while being rotated through 360 0. Note: A figure that possess a point symmetry regains its original shape even after being rotated through 180 0.Įg: The capital letter ‘S’ of the English alphabet also possesses a point symmetry as shown:Ĭlearly, for any point ‘P’ on the figure, there exists a point P’ on the figure, which lies directly opposite to ‘P’ such that OP = OP ′. If corresponding to each point ‘P’ on the figure, there exists a point ‘P’ on the other side of centre, which is directly opposite to the point ‘P’ and lies on the figure. Note: The following letters of the English alphabet have one or more line of symmetry:Ī figure is said to be symmetric about a point ‘O’ called the centre of symmetry. In the figure, the rectangle ABCD is symmetrical about the lines PR&QSĪ square has four lines of symmetry- its two diagonals and the line joining the mid-points of its opposite sides.Ī circle has an infinite number of lines of symmetry- each one of its diameter is a line of symmetry. Thus, we define: If a line divided a given figure into two coincidental parts, then we say that the figure is symmetrical about the line and the line is called the axis of symmetry or line of symmetry.Įg: A line segment (say AB) is symmetrical about its perpendicular bisector (say PQ) as shown in the below figureĪn isosceles triangle ABC is symmetrical about the bisector AD of the angle included between the equal sidesĪ rectangle has two lines of symmetry, each one of which is the line joining the mid-points of opposite sides. Such figures are said to posses linear symmetry or reflection symmetry. REFLECTION SYMMETRY OR LINEAR SYMMETRYĬlearly, if each of these figures is folded along the dotted line, then the pair of the figure on one side of the dotted line falls exactly over the other part i.e., in each figure, the dotted line divides the figure into two coincident parts called the mirror images of each other.
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