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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