Education Technology

Geometry: Side-Side-Angle: The Ambiguous Case

by Texas Instruments


  • Students will identify the conditions necessary to determine a unique triangle when given two sides and a non-included angle (SSA).
  • Students will justify why SSA is not sufficient to establish congruence of two triangles.


  • triangle
  • angle
  • congruence
  • Side-Angle-Side Congruence Theorem
  • Angle-Angle-Side Congruence Theorem

About the Lesson

This lesson involves manipulating the length of a side of a triangle and the non-included angle to identify the conditions that are necessary to determine a unique triangle. As a result students will:

  • Be given two sides and the non-included angle, and they will change the size of the given angle to determine the conditions necessary to determine a triangle.
  • Conclude that uniqueness is a necessary condition for the congruence of two triangles.