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Congruent Polygons

Congruent Polygons. Similar Polygons. Congruent polygons are polygons that are the same size and same shape. They arise from isometric transformations otherwise known as isometries. These transformations preserve length and angular measurement. There are 3 types of isometries:. ROTATIONS.

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Congruent Polygons

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  1. Congruent Polygons Similar Polygons

  2. Congruent polygons are polygons that are the same size and same shape. They arise from isometric transformations otherwise known as isometries. These transformations preserve length and angular measurement. There are 3 types of isometries: ROTATIONS TRANSLATIONS REFLECTIONS Notice that the sides of the corresponding are congruent and so are the corresponding angles.

  3. A F B G E J D I C H To prove that 2 polygons are congruent: corresponding sides must be congruent corresponding angles must be congruent If just one of these turns out not to be the case then the polygons are not congruent.

  4. A F B G E J D I C H As a result of 2 polygons being congruent there are 4 consequences: corresponding sides are congruent corresponding angles are congruent perimeters are equal areas are equal

  5. REDUCTION ENLARGEMENT Similar polygons are polygons that are the same shape but not the same size. They arise from transformations of similitude and are sometimes referred to as dilatations. They can be enlargements or reductions. These transformations preserve angular measurement and the ratio of corresponding sides remain constant.

  6. F G J A B H I E D C To prove that 2 polygons are similar: ratios of corresponding sides must be equal corresponding angles must be congruent ABCDE ~ FGHIJ If just one of these turns out not to be the case then the polygons are not similar.

  7. A F B G E J D I C H As a result of 2 polygons being similar there are 4 consequences: ratio of the corresponding sides are equal corresponding angles are congruent ratio of the perimeters equals ratio of corresponding sides ratio of the areas equals the square of the ratio of the corresponding sides

  8. It is not just plane figures that can be congruent and similar – so can solids like cubes, prisms, cylinders, cones, etc. When 2 corresponding solids are congruent, it means they have the same size and shape and we can make the following conclusions: corresponding segments are congruent areas are equal volumes are equal ratio of lengths of corresponding sides equals 1 (k = 1) When 2 corresponding solids are similar, it means they have the same shape and we can make the following conclusions: corresponding segments are proportional ratio of areas is equal to the square of the ratio of lengths of corresponding sides ratio of volumes is equal the cube of the ratio of lengths of corresponding sides

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