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 ABC PQR, the written order fixes A P, B Q, C R. **Triangle test** | **Corresponding information required** SSS | Three equal sides. SAS | Two equal sides and their equal included angle. ASA or AAS | Two equal angles and an equal corresponding side. RHS | Right angles, equal hypotenuses and one equal corresponding shorter side. Example If AB=PQ=4 cm, AC=PR=7 cm, and BAC= QPR=50, then ABC PQR (SAS). Therefore BC=QR and ABC= PQR. AAA determines shape but not size. Two sides and a non-included angle do not give a general congruence test. List the matched facts before naming the test.

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 \(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\).

If \(AB=PQ=4\text{ cm}\), \(AC=PR=7\text{ cm}\), and \(\angle BAC=\angle QPR=50^\circ\), then \(\triangle ABC\equiv\triangle PQR\) (SAS). Therefore \(BC=QR\) and \(\angle ABC=\angle PQR\).

AAA determines shape but not size. Two sides and a non-included angle do not give a general congruence test. List the matched facts before naming the test.

Correspondence and congruence

Correspondence and congruence

Triangle test	Corresponding information required
SSS	Three equal sides.
SAS	Two equal sides and their equal included angle.
ASA or AAS	Two equal angles and an equal corresponding side.
RHS	Right angles, equal hypotenuses and one equal corresponding shorter side.