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The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles.
The shape and size of a triangle can be uniquely determined up to congruence by specifying the lengths of two sides and the angle between them (SAS) or two angles and the side between them (ASA). Specifying two angles and an adjacent side (AAS) also works, but specifying two sides and an adjacent angle (SSA) usually gives two different possible ...
It can be shown that two triangles having congruent angles (equiangular triangles) are similar, that is, the corresponding sides can be proved to be proportional. This is known as the AAA similarity theorem. [2]
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English: This diagram illustrates the geometric principle of angle-angle-side triangle congruence: Given triangle ABC and triangle A'B'C', triangle ABC is congruent with triangle A'B'C' if and only if angle CAB is congruent with C'A'B' and angle BCA is congruent with B'C'A' and BC is congruent with B'C'.
A reflection in a line is an opposite isometry, like R 1 or R 2 on the image. Translation T is a direct isometry: a rigid motion. [1] In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.
All pairs of congruent triangles are also similar, but not all pairs of similar triangles are congruent. Given two congruent triangles, all pairs of corresponding interior angles are equal in measure, and all pairs of corresponding sides have the same length. This is a total of six equalities, but three are often sufficient to prove congruence ...
The smallest 5-Con triangles with integral sides. In geometry, two triangles are said to be 5-Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths (of non-corresponding sides). The 5-Con triangles are important examples for understanding the solution of triangles. Indeed, knowing ...