Congruent triangles are identical in shape and size; similar triangles are enlargements of one another. A proof quotes one of the tests below, names the triangles with vertices in corresponding order, then reads off the remaining equal sides, equal angles or side ratios.

**Tests for congruent triangles: \(\triangle ABC\equiv\triangle XYZ\)**

\(AB=XY\)
\(AC=XZ\)
\(\angle BAC=\angle YXZ\) (included angle)

\(\angle BAC=\angle YXZ\)
\(\angle ABC=\angle XYZ\)
\(AB=XY\) (included side)

\(\angle ABC=\angle XYZ=90^\circ\)
\(AC=XZ\) (hypotenuse)
\(BC=YZ\)

After proving congruence, every pair of corresponding sides and angles is equal. Name the triangles in corresponding vertex order before quoting the test.

SSS CONGRUENCE TEST	SAS CONGRUENCE TEST	AAS CONGRUENCE TEST	RHS CONGRUENCE TEST

Test	What must match	Sketch
SSS
SAS
ASA
RHS

Congruency Tests

Congruency Tests

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