Definition 1: Two geometric figures are congruent or equivalent if the are the same shape and size.

This means that if you cut out the second figure with scissors, you can place it over the first figure and they match exactly (you are allowed to turn the piece of paper over).

The symbol for congruency is \cong .

For example, {\triangle \text{ABC}}\, \cong \,\triangle \text{DEF} is read "triangles АВС and DEF are congruent".  

Interactivity 1: Congruent triangles   Directions for interactivity

Click and drag the slider buttons to change the size. Click and drag the zoom button as needed.

Click and point blue points to move and rotate triangle T1 to match triangle T2.
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The symbol \cong comes from \sim plus =     (similar plus equal).

Mathematically, two geometric figures or objects are congruent if there is a combination of a translation (shift), rotation and/or reflection so that the figures match exactly.  (In the above, 'cutting with scissors' is a translation and rotation and 'turning the paper over' is a reflection :-) .)

Deductions (because they are the same shape...)

  • Two sides (line segments) \overline{AB} and \overline{CD} of the same or different geometric figures are congruent if the are the same length, that is if: |\overline{AB}| = |\overline{CD}| .
  • Two angles <ABC and <DEF in the same or different geometric figures are congruent if they are of equal size (with congruency the direction of the angle is NOT important, i.e. <ABC \cong <CBA ).

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Page last modified on September 14, 2008, at 11:08 PM