For the congruence of triangles we have three criteria to indicate that really two or more triangles are congruent, these are the criteria of congruence **SAS** (side-angle-side), the criterion **ASA** (angle-side-angle) and the **SSS** (side-side-side) criterion.

It should be noted that some authors call them “postulates of congruence”, and others, “theorems of congruence”; but remember that it is only a question of agreements according to the level of formalism of the course: these variations do not affect the concepts in their usefulness. (Colonia, 2004, 65).

## Criteria of congruence

#### Criteria SAS (side-angle-side)

Two triangles are congruent if they respectively have two sides congruent and the angle between the two sides mentioned.

\Delta ABC \cong \Delta DEF

\overline{AB} \cong \overline{DE}

\measuredangle B \cong \measuredangle E

\overline{BC} \cong \overline{EF}

#### Criteria ASA (angle-side-angle)

Two triangles are congruent if they respectively have two angles congruent and the side between both angles.

\Delta GHI \cong \Delta JKL

\measuredangle G \cong \measuredangle J

\measuredangle I \cong \measuredangle L

\overline{GI} \cong \overline{JL}

#### Criteria SSS (side-side-side)

Two triangles are congruent if they have three sides congruent respectively.

\Delta MNÑ \cong \Delta OPQ

\overline{M\tilde{N}} \cong \overline{OP}

\overline{MN} \cong \overline{OQ}

\overline{N\tilde{N}} \cong \overline{QP}

And that’s it, those are the criteria of congruence of triangles.

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