Congruent Triangles - Two sides and included angle (SAS)

Definition: Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.

There are five ways to test that two triangles are congruent. This is one of them (SAS). For a list see Congruent Triangles. If any two corresponding sides and their included angle are the same in both triangles, 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 two sides and included angle are drawn in thick blue lines to indicate they are the parts being used to test for congruence.

What does this mean?

Because the triangles are congruent:
  1. the third sides are also equal (PQ = LM)
  2. the remaining two correspnding angles are equal (P=L and Q=M)

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 above, 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