Understand and prove the triangle interior angle sum theorem and the exterior angle sum theorem through discovery and the use of parallel lines cut by a transversal

Big Ideas: Students will be able to use the triangle angle sum theorem to solve problems. Students will be able to prove the triangle angle sum theorem. Students will discover the triangle angle sum theorem and then use it to solve problems. Students will then prove the theorem using parallel lines cut by a transversal. Students will also learn about exterior angles and their properties. This lesson should take place after students have learned basic constructions, parallel lines cut by a transversal, and inequalities in one triangle. This lesson leads to lessons involving isosceles and equilateral triangles. Students will also deepen their skills for developing proofs. Vocabulary: parallel lines cut by a transversal, triangle angle sum theorem, interior angle, exterior angle Special Materials: popsicle sticks or straws ruler protractor compass