Lines of reflection symmetry6/20/2023 ![]() ![]() So to go back over, what exactly reflectional symmetry is? Is it's a more specific definition of symmetry where you can reflect half of the figure back onto itself. An object and its image are always at the same distance from the surface of a mirror, which is called the mirror line. If we're talking about a scalene triangle, well let's say we gave these sides lengths of 2, 5 and 8 there are no lines of symmetry of reflectional symmetry of the scalene triangle. ![]() We look at an Isosceles triangle, if I label these two sides as being congruent there's only one line of symmetry because if I drew in another line here, it would not be a mirror image of itself. What about an equilateral triangle? Well an equilateral triangle similarly I can draw this line through the vertex perpendicular to the opposite side and I could draw in two more so an equilateral triangle will have 3 lines reflectional symmetry. I could also draw a horizontal line of symmetry I can also draw in some diagonal lines of symmetry and those would enable me to fold the figure back onto itself, so this regular pentagon had 5, the square has 4 lines of symmetry. If we move onto a square I see that I could draw in a line of symmetry through the half of these 2 sides and I could fold it. I could draw a perpendicular through each one of these vertices perpendicular to the opposite side for a total of 5 lines of reflectional symmetry. Here we're being asked to find the lines of reflectional symmetry which means, what line could I draw on this pentagon so that I could fold the pentagon back onto itself and have an identical image? Well I see that I could draw a line of reflection right there which would enable me to fold my pentagon over onto itself. Let's apply what we know about reflectional symmetry to some specific examples. We also describe reflectional symmetry using the term line symmetry, so those 2 are interchangeable. If that isometry is a reflection then a figure has reflectional symmetry, so another way of thinking about reflectional symmetry is that half the figure is a mirror image of the other half. Check out these interesting articles to know about reflection symmetry and its related topics. A figure can have one or more lines of reflection symmetry depending on its shape and structure. Reflection symmetry can also be observed in inkblot paper. There are many objects in Geometry and in real life that have symmetry, but how do we define symmetry? Well an object has symmetry if there exist an isometry so reflection a rotation maybe even a translation that maps the figure back onto itself. An object and its image are symmetrical with respect to its mirror line. ![]()
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