Lesson objective: Find missing angle measures in a triangle using the angle sum for triangles. In addition, students will use the Triangle Inequality Theorem to determine if a triangle will form when given the measures of the three sides.

This lesson helps to build procedural skill with looking at the attributes of a triangle and determining the values for the angles and sides that allow a triangle to be constructed. Drawings are used here because it shows how triangles are constructed using given measures of sides or angles. This work develops students' understanding that the sum or 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 and make use of structure) as they find the measure of a third angle of a triangle when given the other two angles and determine the range of values for the length of the third side of a triangle when given the other two sides.

**Key vocabulary:**

- acute triangle
- acute angle
- adjacent angle
- angle
- base angle
- isosceles triangle
- obtuse angle
- obtuse triangle
- right angle
- right triangle
- side
- straight angle
- supplementary angle
- Triangle Inequality Theorem
- triangle angle sum
- vertex

**Special materials needed:**

- protractor
- ruler