Unit Plan 22 (Grade 8 Math): Angle Relationships & Triangle Facts
8th graders explore angle relationships in triangles and parallel-line diagrams, using informal proofs to show the triangle sum and exterior angle theorems. They solve for unknown angles and justify reasoning with clear geometric arguments.
Focus: Use informal arguments about angle sum of triangles, exterior angles, and angles formed by parallel lines/transversals.
Grade Level: 8
Subject Area: Mathematics (Geometry)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This week is all about angle sense. Students investigate how angles behave when parallel lines are cut by a transversal, why the sum of the interior angles of a triangle is 180°, and how a triangle’s exterior angle relates to its remote interior angles. Emphasis is on informal arguments (folding, tracing, and parallel-line reasoning) and clear justifications in their own words. Students finish the week solving unknown-angle problems with brief written reasoning.
Essential Questions
- Which angle pairs are always equal or supplementary when a transversal crosses parallel lines, and why?
- Why do the interior angles of a triangle add to 180°?
- Why is a triangle’s exterior angle equal to the sum of its two remote interior angles?
- How do I show my angle work with a convincing argument (diagram + words), not just a number?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Identify and justify angle relationships for parallel lines cut by a transversal (corresponding, alternate interior/exterior, same-side interior; linear pairs; vertical angles).
- Use informal arguments (paper folds, tracing, parallel-line constructions) to show that the sum of interior angles of a triangle is 180°.
- Explain and apply the exterior angle theorem: the exterior angle equals the sum of the two remote interior angles.
- Solve for unknown angles in multi-step diagrams and triangles, writing a brief justification that cites a valid relationship.
Standards Alignment — CCSS Grade 8
- 8.G.5: Use informal arguments to establish facts about the angle sum and exterior angle of a triangle, about the angles created when parallel lines are cut by a transversal, and the angle–angle criterion for similarity of triangles. (This unit emphasizes triangle sum, exterior angles, and parallel-line angle relations; AA similarity is foreshadowed, then developed more in similarity units.)
Success Criteria (student-friendly)
- I can name angle pairs and state whether they are congruent or supplementary, and explain why.
- I can show, with a fold/trace or parallel-line reasoning, that the angles in any triangle add to 180°.
- I can use the exterior angle relationship to find unknown angles and explain my steps.
- I can write a two- to three-sentence justification that someone else can follow.