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Symmetry. In mathematics, especially in geometry and its applications, an object is said to have symmetry if it can be divided into two identical halves. For example, look at the given picture of a flower: If we were to draw an imaginary line in the middle of it, we could divide it into two equal parts like this:
Example 1: the square (lines of symmetry) Draw all of the lines of symmetry for the square below. Locate the centre of the 2D shape. Draw a small x x in the centre of the square (this does not have to be exact) 2 Use a ruler to visualise a horizontal and/or vertical line of symmetry through the centre of the shape.
4 Draw a line from each vertex through the center and check for line symmetry. 5 State the number of lines of symmetry. The equilateral triangle has 3 3 lines of symmetry. An equilateral triangle has 3 3 equal sides and 3 3 equal angles, so it will have 3 3 lines of symmetry.
Symmetry And Line Of Symmetry: An Introduction. In geometry, symmetry is defined as a balanced and proportionate similarity that is found in two halves of an object. It means one-half is the mirror image of the other half. The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
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Example 3: using angles. Show that the hexagon below has no lines of symmetry. Locate the centre of the 2D shape. Show step. Draw a small x x in the centre of the hexagon (this does not have to be exact): Use a ruler to visualise a horizontal and/or vertical line of symmetry through the centre of the shape. Show step.
the same distance from the central point. but in the opposite direction. Check to see if the equation is the same when we replace both x with −x and y with −y. Example: does y = 1/x have Origin Symmetry? Start with: y = 1/x. Replace x with − x and y with − y: (−y) = 1/ (−x) Multiply both sides by − 1:
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Symmetry in a figure exists if there is a reflection, rotation, or translation that can be performed and the image is identical. Rotational symmetry exists when the figure can be rotated and the image is identical to the original. Regular polygons have a degree of rotational symmetry equal to 360 divided by the number of sides.
