Lesson Plan

Explain why the sum of the interior angles of any triangle is 180 degrees, using an argument based on arranging copies of the triangle's angles along a straight line and connecting that arrangement to parallel lines and transversals

Explain why an exterior angle of a triangle equals the sum of the two non-adjacent interior angles, using the triangle angle sum property

Identify and explain the angle relationships created when a transversal crosses two parallel lines: corresponding angles are equal, alternate interior angles are equal, alternate exterior angles are equal, and co-interior (same-side interior) angles are supplementary

State the Angle-Angle (AA) criterion for triangle similarity: if two angles of one triangle are equal to two angles of another triangle, the triangles are similar

Explain why only two pairs of equal angles are needed to guarantee similarity, using the triangle angle sum property to show the third pair must also be equal

8.G.A.5

8.G.A.5: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.