Lesson objective: Extend understanding of angle relationships to informally prove the angle sum of triangles.

Students bring prior knowledge of angle relationships from 7.G.B.5 and 8.G.B.5. This prior knowledge is extended to triangles formed from two transversals and parallel lines as students prove the angle sum of triangles. A conceptual challenge students may encounter is determining an effective and concise way to represent their proof.

The concept is developed through work with a visual model of a triangle created from two transversals, which gives students the opportunity to use angle relationships (alternate exterior, alternate interior, corresponding, vertical) to make connections to the sum of interior angles of a triangle.

This work helps students deepen their understanding of equivalence because students use equal angle measures created from transversals and parallel lines to create and defend their argument.

Students engage in Mathematical Practice 3 (construct viable arguments and critique the reasoning of others) as they create and justify their proof and critique the proofs of other students.

**Key vocabulary:**

- alternate exterior angles
- alternate interior angles
- corresponding angles
- transversal
- triangle angle sum
- triangle