The Concept of Congruence Topic Index | Geometry Index | Regents Exam Prep Center

Congruence - Congruent

 You walk into your favorite mall and see dozens of copies of your favorite CD on sale.  All of the CDs are exactly the same size and shape.  In fact, you can probably think of many objects that are mass produced to be exactly the same size and shape.

Objects that are exactly the same size and shape are said to be congruent.
Congruent objects are duplicates of one another.
If two mathematical figures are congruent and you cut one figure out with a pair of scissors, it will fit perfectly on top of the other figure.

 Mathematicians use the word congruent to describe geometrical figures.   -- If two quadrilaterals (4 sided) are the same size and shape,           they are congruent.   -- If two pentagons (5 sided) are the same size and shape,           they are congruent.   -- If two polygons (any number of sides) are the same size and shape,           they are congruent.   -- If two line segments are the same length (they already are the same           shape), they are congruent.

 The mathematical symbol used to denote congruent is . The symbol is made up of two parts: which means the same shape (similar) and which means the same size (equal).
 Congruent Symbol

 When you are looking at congruent figures, be sure to find the sides and the angles that "match up" (are in the same places) in each figure.  Sides and angles that "match up" are called corresponding sides and corresponding angles.   In congruent figures, these corresponding parts are also congruent.  The corresponding sides will be equal in measure (length) and that the corresponding angles will be equal in degrees.

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