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Congruent figures

Basic shapes

Japanese school year: Elementary 5

What you learn

Investigate properties of congruent figures that match exactly when overlapped, including corresponding sides, angles, and vertices. Learning to identify figures with identical shape and size provides essential groundwork for geometric reasoning and construction. Reviewing how to measure lengths and angles is recommended.

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Key points

This defines geometric congruence. Two figures are called congruent if one can be moved (translated, rotated, or reflected) to fit perfectly over the other.

This states the fundamental property of congruent figures. In congruent shapes, corresponding sides are equal in length, and corresponding angles are equal in measure.

This notation indicates that △ABC\triangle ABC and △DEF\triangle DEF are congruent. The vertices must be written in corresponding order, such as matching vertex AA with DD.

△ABC≡△DEF\triangle ABC \equiv \triangle DEF

Choose a set to practice.