Triangle Congruence

Also called

congruent triangles · congruence of triangles · SSS · SAS · ASA · AAS · RHS · SSA is not a rule · side side side · side angle side · angle side angle · right angle hypotenuse side · corresponding parts of congruent triangles · CPCT · included angle · included side · superposition · सर्वांगसम त्रिभुज · सर्वांगसमता · भुजा-कोण-भुजा

Topics

• Two triangles are congruent if one can be placed exactly on the other: all corresponding sides and angles are equal.
• SSS: if the three sides of one triangle equal the three sides of another, the triangles are congruent.
• SAS: two sides and the angle included between them fix a triangle, so matching them gives congruence.
• ASA: two angles and the side included between them fix a triangle; AAS follows because the third angle is then known.
• RHS: two right triangles are congruent if their hypotenuses and one pair of other sides are equal.
• SSA is not a congruence rule: two sides and a non-included angle can be shared by two different triangles.
• Once two triangles are shown congruent, their remaining corresponding parts are equal (CPCT).

About this model

A GLB file of about 186 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.

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