How do you prove something is congruent? As an example explain how to show that two triangles are congruent.

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In geometry, two polygons are said to be congruent if they are exact copies or exact mirror images of each other.

Triangles (three-sided polygons) are congruent if they follow any of the five following rules:

  1. SSS:  All three sides are equal
  2. SAS:  2 sides and their included angle are equal
  3. ASA:  A pair of angles and their included side are equal
  4. AAS:  2 corresponding angles and their non-included side are equal
  5. HL:  The hypotenuse and 1 leg of a right triangle are equal

Another way to explain congruency is to say that if you made a paper cutout of the two polygons they would exactly fit when placed on top of each other, except in the case of mirror images, one must be turned over.

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