Definition: We say that a geometric figure is completely determined by a set of conditions if all figures created under those conditions are congruent*.

Rules: Using the term "completely determined" usually means that all of the given conditions are necessary. That is, if one or more of the conditions are missing then non-congruent figures can be constructed (see example 2 below).

 

Examples:

  1. A square is completely determined by the length of a side.
    • This means that all squares with one side equal are congruent.
    • Example: All squares with side а=4cm are congruent.
  2. A rhombus is completely determined by the length of a side and the size of one angle."
    • This means that all rhombi with one side equal and one angle equal are congruent.
    • Example: All rhombi with side а=9cm and interior angle \alpha=37^\circ are congruent.
    • This also means that two rhombi with side а=9cm don't have to be congruent (missing condition for angle).

* Let's remember: 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.


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Page last modified on September 14, 2008, at 11:53 PM