Lesson objective: Determine if a given set of attributes for a triangle produce a unique triangle, more than one triangle, or no triangle.

This lesson helps to build procedural skill with using the triangle angle sum and the Triangle Inequality Theorem. Visual representations are used here because students use the drawings to write equations that show the relationships among the angles and sides of the triangle. This work develops students' understanding that the sum of the angles in a triangle is 180\(^\circ\)and that the sum of the lengths of two sides of a triangle is greater than the length of the third side of the triangle.

Students engage in Mathematical Practice #7 (look for and make use of structure) as they determine the conditions that create a unique triangle, more than one triangle, or no triangle.

**Key vocabulary:**

- acute triangle
- angle
- base angle
- isosceles triangle
- obtuse triangle
- right triangle
- side
- triangle angle sum
- Triangle Inequality Theorem

**Special materials needed:**