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Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.

Congruent (geometry)

From AoPSWiki

Congruency is a property of multiple geometric figures.

Intuitive Definition

Two geometric figures are congruent if one of them can be turned and/or flipped and placed exactly on top of the other, with all parts lining up perfectly with no parts on either figure left over. In plain language, two objects are congruent if they have the same size and shape.


A collection of isometries.
A collection of isometries.

Technical Definition

Two geometric objects are congruent if one can be transformed into the other by an isometry, such as a translation, rotation, reflection or some combination thereof.

See also

Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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