The term symmetry comes from a Greek word ‘sun + metron’, which later transformed into Latin ‘symmetria’, meaning ‘with measure’. This axis is known as the axis of symmetry. If you fold the body along this axis, you will get two or more similar figures. Line of Symmetry DefinitionĪ line of symmetry is an imaginary line or axis which passes through the center of a body or an object. Doesn’t it look symmetrical from either side if you draw an imaginary axis along your face? Now, let us understand what a symmetrical body or simply, symmetry means. Or, if an octopus is cut along its head, it will also produce similar shapes. For example, if a starfish is cut across its limbs, you will get similar shapes. A symmetrical body is an object or thing that can be cut along a particular axis, producing similar shapes. Have you wondered why your mirror reflection appears symmetrical while a few objects do not? Or could you guess what the similarity between two marine animals – a starfish and an octopus are? If you guessed they have a symmetrical body, then you are correct. Similarly, the shape would not alter if a mirror were positioned along the line. This indicates that both half of the object would perfectly match if you folded it along the line. Can you name its Order and degrees of rotation?Ī hexagon shows Order 6 rotational symmetry, with 60 degrees of rotation.Line of Symmetry is a line that splits a form exactly in half. Picture a hexagonal shape, like a honeycomb or a section of a soccer ball. The sea star is Order 5, using 72 degrees of rotation. Getting back to our sea stars, can you figure out their Order of rotational symmetry and their degrees of rotation? Remember, a sea star has five arms. You can get the degree of rotation if you know the Order, by dividing:ģ60 ° O r d e r \frac d e g ree − o f − ro t a t i o n 360° = order So, the cell phone's rectangular shape rotated 180° two times Order 2. You can do that same move again to return to the original shape. Concentrating only on its outline, what happens when you rotate (spin) the phone halfway around a complete circle? A rectangle has Order 2 Take a rectangular cell phone, for example. Very often you can find the degrees of rotation by physically rotating the object, if it is something in your daily life. The number of degrees you must rotate the object around its center is key to finding its Order of rotational symmetry, but it also tells you how much to rotate the object to make it match its original position. You can do that 10 times in making one complete rotation. Without drawing it, can you say what the Order of rotational symmetry is for a regular decagon, a 10-sided polygon? It is Order 10, meaning you can rotate the figure 36° and match it to the original. What about this regular pentagon? What is its rotational symmetry? A pentagon has Order 5ĭid you say it is Order 5? Have you noticed a pattern? For the regular polygons, the Order of rotational symmetry is equal to the number of sides of the polygons. We can do that four times, so a square has Order 4. To go from the first drawing to the second, we need only rotate the object 90°. So it has rotational symmetry of Order 3.Ĭan you figure out the Order of rotational symmetry for the square below? A square has Order 4 The equilateral triangle will match three times in rotating (turning) around its center. How many times will it match itself when rotated around its center? Equilateral triangle with Order 3 In mathematics, all the regular polygons have rotational symmetry. Many everyday objects show rotational symmetry. The only misfit is Order 7, since 360° does not divide evenly by 7. This is because 360° has so many factors. You may also notice just how many Orders are possible. No object has rotational symmetry of Order 1. You may notice that no Order 1 exists this would be a shape that has to turn completely around ( 360°) to look the same. Order of symmetryĬommon orders and the amount the object rotates are: If it only matches up twice, it is Order 2 if it matches the original shape three times, it is Order 3, and so on. The order of symmetry is a number used to describe how many times the object will appear to be the same while rotating through 360°. The rectangle that is your mathematics textbook can be rotated around that center to find its rotational symmetry. Can you find a spot on it that allows the book to balance on your index finger? When you find that spot, you have the center of the object. The center, pivot, or center of balance are all ways to describe the single point on an object around which the object can turn, rotate or spin.
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