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Geometry: Congruence

Terms

Congruence

Corresponding Parts of Triangles

AA  -  A method for proving similarity of triangles: if two angles are congruent to their corresponding parts in another triangle, then the triangles are similar.
AAS  -  A method for proving congruence of triangles: if two angles and a side not included by those angles are congruent to their corresponding parts in another triangle, then the triangles are congruent.
ASA  -  A method for proving congruence of triangles: if two angles and their included side are congruent to their corresponding parts in another triangle, then the triangles are congruent.
Congruent Triangles  -  Triangles whose corresponding angles and sides are all congruent.
Congruent Polygons  -  Polygons whose corresponding sides and interior angles are all congruent.
Corresponding Parts  -  The angles or sides in a polygon organized such that each angle and each side coincides with exactly one angle or side in another polygon--the pairs of angles and sides in each polygon are called corresponding parts.
Hypotenuse-Leg  -  A method for proving congruence of right triangles: if one leg and the hypotenuse are congruent to their corresponding parts in another right triangle, the right triangles are congruent.
SAS  -  A method for proving congruence or similarity of triangles: if two sides are congruent or proportional and their included angle is congruent to their corresponding parts of another triangle, then the triangles are congruent or similar, respectively.
Similar Triangles  -  Triangles whose corresponding angles are congruent and whose corresponding sides are proportional. Congruence is a subset of similarity.
SSS  -  A method for proving the congruence or similarity of triangles: if the three sides of a triangle are congruent to their corresponding parts, then the triangles are congruent. If the three sides of a triangle are proportional to their corresponding parts in another triangle, then the triangles are similar.

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