Translate the first figure by this vector so that these two vertices match. Second, draw a vector from one of the vertices of the one of the figures to the corresponding vertex of the other figure.First, match and label the corresponding vertices of the two figures.for n sides and n angles.Ĭongruence of polygons can be established graphically as follows: Two polygons with n sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle. (The ordering of the sides of the blue quadrilateral is "mixed" which results in two of the interior angles and one of the diagonals not being congruent.)įor two polygons to be congruent, they must have an equal number of sides (and hence an equal number-the same number-of vertices). All three have the same perimeter and area. The orange and green quadrilaterals are congruent the blue is not congruent to them. (Most definitions consider congruence to be a form of similarity, although a minority require that the objects have different sizes in order to qualify as similar.) The related concept of similarity applies if the objects have the same shape but do not necessarily have the same size. In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas.
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