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Congruent Triangles - Three sides equal (SSS)

Definition: Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.

There are five ways to test that two triangles are congruent. This is one of them (SSS). For a list see Congruent Triangles. If all three sides in one triangle are the same length as the corresponding sides in the other, then the triangles are congruent.

Try this Drag any orange dot at P,Q,R. The other triangle LMN will change to remain congruent to the triangle PQR.
Notice that the the three sides are drawn in thick blue lines to indicate they are the parts being used to test for congruence.

What does this mean?

  1. Since all three corresponding sides are the same length, we can be sure the triangles are congruent.
  2. Because the triangles are congruent, this means that the three angles at P,Q and R are equal to the angles L,M and N respectively.

But don't forget:

Two triangles, congruent because all three sides are the same length, but one flipped and rotated Congruent triangles can be rotated and/or mirror images of each other (reflected). (See Congruent triangles.) In the figure on the right, the two triangles have all three corresponding sides equal in length and so are still congruent, even though one is the mirror image of the other and rotated.

Other congruence topics

Congruent Triangles

Congruent Polygons