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

Expert Answers
boblawrence eNotes educator| Certified Educator

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.

kshelor | Student

If I understand your question the definition of congruency is the geometric shape is the same size and same shape.  It doesn't matter if the shapes are different colors, patterned, or turn sideways, they just have to be the same size and same shape.

If you use a Power Point, Smart Notebook, or even an overhead projector, show the students that if you put the first shape on top of the second shape, the two shapes should be exactly the same.  This proves they are congruent or they are not.