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
If any two corresponding sides and their included angle are the same in both triangles, then the triangles are congruent.
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:
- the third sides are also equal (PQ = LM)
- the remaining two correspnding angles are equal (P=L and Q=M)
But don't forget:
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.
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