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Congruent Triangles - Two angles and included side (ASA)

Definition: Triangles are congruent if any two angles and their included side are equal in both triangles.

There are five ways to test that two triangles are congruent. This is one of them (ASA). For a list see Congruent Triangles. If any two angles and the included side 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 angles and included side are drawn in thick blue lines to indicate they are the parts being used to test for congruence.

What does this mean?

  1. Since two angles and the included side are equal in both triangles, we can be sure the triangles are congruent.
  2. Because the triangles are congruent, the third angles (R and N) are also equal
  3. Because the triangles are congruent, the remaining two sides are equal (PR=LN, and QR=MN)

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