When you are drawing a reflected shape, you need to use this systematic approach: In the diagram, the line connecting point A to A’ is called a construction line and illustrates these rules: The distance between A and the mirror line is the same as the distance between A’ and the mirror line and the construction line is perpendicular to the mirror line (shown by the small square at its centre). The line that connects a point with its reflection is perpendicular (at right angles) to the mirror line. The letter A, for example, has a single vertical line of symmetry, from the apex to the base:Įach point and its reflection are exactly the same distance from the mirror line. This means that if you were to place a mirror along the line of symmetry, then the reflection of the shape in the mirror would be identical to the shape without the mirror in place. Line symmetry is a form of reflection (which is covered later in this page) and is sometimes referred to as mirror symmetry. The simplest form of symmetry is line symmetry. But if you have a group of shapes all the same as shape G, then shape G would be congruent with all of those shapes.Ī shape can be described as symmetrical if it has a property that mathematicians refer to as symmetry. Shape G for example is not congruent with any of the other shapes in our diagram. However, it cannot be described as congruent until there is another shape to compare it to. If you look at Shape A on its own, you can say that it is an irregular hexagon and you can measure its perimeter and area. Shape A cannot be described as ‘congruent’ on its own. In the diagram below, shapes A, B, C and D are all congruent. Two shapes that are congruent have the same size and the same shape. Mathematics is full of complex terminology, but sometimes a complicated term can mean something really simple. Even matching the pattern on a roll of wallpaper involves these geometric ideas. We are faced with these ideas regularly in everyday life, in everything from product design, architecture and engineering, to occurrences in the natural world. These concepts are about how a shape’s position changes, relative to a reference, such as a line or a point. This page explores congruence, symmetry, reflection, translation and rotation. They can undergo transformations, whereby they can change position or size, or ‘aspect ratio’ (how tall and thin or short and wide they are). Plane shapes in two dimensions (drawn on a flat piece of paper for example) have measurable properties apart from just their physical measurements of side lengths, internal angles and area.
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