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Congruence of triangles criteria

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.

side-angle-side-congruence-criterion

\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.

angle-side-angle-congruence-criterion

\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.

congruence-criterion-side-side-side

\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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