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Angle-Side-Angle (ASA) Congruence Theorem

Angle-Side-Angle (ASA) Congruence Theorem

One-page printable reference

See It in Action

Two examples of the idea done right—and one common look-alike that is not right.

EXAMPLE

EXAMPLE

NON-EXAMPLE

Definition

The Angle-Side-Angle (ASA) Congruence Theorem states:


If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.


Two congruent triangles with two corresponding angles and a congruent side. The congruent side is in between the angles. The congruent angles are on the top and left corners of the triangles, and the congruent side is on the left side of the triangles in between the angles.

Key points:

  • The side must be between the two angles.

  • This guarantees that the shape of the triangle is fixed, so the triangles must be congruent.

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