Congruence

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An example of congruence. The two shapes on the left are congruent. The third is similar to the first two, but not congruent, because it needs to be grown to match them. The last shape is neither similar nor congruent.

Numbers are equal, geometrical objects are congruent. Two shapes are congruent if one can be moved or rotated so that it fits exactly where the other one is. If one of the object has to change its size, the two objects are not congruent. They are called similar. Also, every two objects which are congruent are similar at the same time. Geometrical objects can be equal, too, but only if they are in the same place, so an object can only be equal to itself.

Examples:

• all squares that have the same length of their sides are congruent.
• all equilateral triangles that have the same length of their sides are congruent.

Tests for Congruency

• One side and two angles of a triangle are the same on two triangles (ASA congruence)
• All three sides of both triangles are the same (SSS congruence)
• two sides and the angle between them makes 2 triangles congruent (SAS congruence)

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