Triangle Congruence

Related Topics:
Common Core (Geometry)
Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

Common Core: HSG-CO.B.8

When two triangles are congruent, the corresponding sides and the corresponding angles are equal. Conversely, if all six parts of corresponding sides and corresponding angles of the two triangles are congruent, then the triangles are congruent.

However, there is a "shortcut" in which only three pairs of congruent corresponding parts are needed in order to conclude that the triangles are congruent.

SAS Congruence

If two sides and an included angle of one triangle are congruent to two sides and an included angle of another triangle, then the triangles are congruent.

We can show this by using a sequence of rigid motions.

Side-Angle-Side Congruence by basic rigid motions. ASA Congruence
If two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the triangles are congruent.

We can show this by using a sequence of rigid motions.

Angle-Side-Angle Congruence by Basic Rigid Motions.

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SSS Congruence

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Congruent Triangles and SSS
What it means for triangles to be congruent and the Side-Side-Side Congruence. Triangle Congruence - SSS, SAS, ASA and AAS
4 ways of proving that triangles are congruent.

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