Congruence tests

<p class="paragraph-header">Matching vertices</p>
<p>Congruent figures have the same shape and size. The statement \(\triangle ABC\equiv\triangle PQR\) fixes the correspondence \(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\), even when one triangle is turned over or rotated.</p>
<p>Match sides and angles by their endpoints: \(AB=PQ\), \(BC=QR\), \(AC=PR\) and \(\angle BAC=\angle QPR\). A diagram's orientation is not a proof.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center">Test</th><th style="text-align: center; --cell-justify: center">Required corresponding information</th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">SSS</td><td style="text-align: center; --cell-justify: center">Three equal sides.</td></tr><tr><td style="text-align: center; --cell-justify: center">SAS</td><td style="text-align: center; --cell-justify: center">Two equal sides and the equal angle between them.</td></tr><tr><td style="text-align: center; --cell-justify: center">ASA</td><td style="text-align: center; --cell-justify: center">Two equal angles and the equal included side.</td></tr><tr><td style="text-align: center; --cell-justify: center">AAS</td><td style="text-align: center; --cell-justify: center">Two equal angles and an equal corresponding non-included side.</td></tr><tr><td style="text-align: center; --cell-justify: center">RHS</td><td style="text-align: center; --cell-justify: center">Right angles, equal hypotenuses and one other equal side.</td></tr></tbody></table></div></div>
<p>AAA fixes shape but not size. SSA is not a valid general congruence test: the stated angle may not be between the stated sides. State the matched facts, the test and the triangles in corresponding order.</p>

Congruent figures have the same shape and size. The statement \(\triangle ABC\equiv\triangle PQR\) fixes the correspondence \(A\leftrightarrow P\), \(B\leftrightarrow Q\), \(C\leftrightarrow R\), even when one triangle is turned over or rotated.

Match sides and angles by their endpoints: \(AB=PQ\), \(BC=QR\), \(AC=PR\) and \(\angle BAC=\angle QPR\). A diagram's orientation is not a proof.

AAA fixes shape but not size. SSA is not a valid general congruence test: the stated angle may not be between the stated sides. State the matched facts, the test and the triangles in corresponding order.

Correspondence and congruence tests

Correspondence and congruence tests

Test	Required corresponding information
SSS	Three equal sides.
SAS	Two equal sides and the equal angle between them.
ASA	Two equal angles and the equal included side.
AAS	Two equal angles and an equal corresponding non-included side.
RHS	Right angles, equal hypotenuses and one other equal side.