Corresponding
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Because if you take a triangle and double the length of each side, you get a much bigger triangle which is therefore not congruent (they do not match in every respect, even though the angles are replicated). In this case they are called "similar".
Any two corresponding sides in two similar figures have a common ratio called the scale factor. Since the figures are similar, the ratios of the lengths of corresponding sides of the figures are equal. 1. Match a side of both figures, 2. write the proportions 3. substitute the values 4. Write the cross product 5. Divide both sides by a common factor 6. simplify 7. Convert improper fraction into mixed number
Line Symetry
If the triangles are congruent and you match the hypotenera the right way, you can get a rectangle. If the triangles are not congruent, you can't even necessarily get a quadrilateral.
Any symmetrical figure has two halves that match. By definition, you cannot have more than two halves of a figure.