Geometry: Side-Side-Angle: The Ambiguous Case

Objectives

• 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.

Vocabulary

• 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.