Lesson objective: Justify angle relationships of a triangle.

This lesson provides an opportunity for students to apply their knowledge and understanding of angle relationships to a mathematical situation. Students are asked to provide a justification of the relationship between the exterior angle of a triangle and its remote interior angles. They will construct a viable argument on whether this relationship applies to all types of triangles.

Key Concept students will use:

- Angles created when parallel lines are cut by a transversal have special relationships, including congruence, and we can use the idea of translating parallel lines to other parallel lines that are closer and closer to one another.

Skills students will use:

- Facts about supplementary, complementary, and adjacent angles to write and solve equations about missing angles; (Grade 7, Unit 14)

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they make conjectures about the exterior angle theorem and build a logical progression of statements to verify those conjectures.

**Key vocabulary: **

- exterior angle
- interior angle
- remote interior angle
- Exterior Angle Theorem

**Special materials needed:**