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Explain the congruence of triangles.
Congruence of triangles :
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
Sufficient evidence for congruence between two triangles can be shown through the following comparisons:
SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
AAS (Angle-Angle-Side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°.
RHS (Right-angle-Hypotenuse-Side): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides are equal in length, then the triangles are congruent.
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