Correspondence and congruence

Congruent figures have the same shape and size. Translation, rotation or reflection can change their position or orientation without changing their lengths or angles. In \(\triangle ABC\equiv\triangle PQR\), the written order fixes \(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\).

Example

If \(\triangle ABC\) is congruent to \(\triangle PQR\) in that order, \(AB=PQ\), \(BC=QR\), \(AC=PR\), and corresponding angles are equal. If \(BC=5\text{ cm}\), then \(QR=5\text{ cm}\).

Congruence requires equal size as well as equal shape. Two triangles with the same angles but different side lengths are similar, not congruent. Match vertices by their corresponding sides and angles, rather than their left-to-right positions.