Polygon Architects

An 8th-grade geometry sequence focused on the derivation and application of polygon angle properties. Students progress from the Triangle Sum Theorem to general formulas for interior and exterior angles of any polygon, ultimately applying these properties to solve complex algebraic problems.

Triangle Sum Secrets

Students explore the interior angles of triangles through hands-on inquiry and formal reasoning. They discover that the sum of interior angles is always 180 degrees using physical manipulation and parallel line properties.

External Perspectives

Learners investigate the relationship between interior and exterior angles, discovering the Exterior Angle Theorem. They practice calculating exterior angles and solving linear equations based on these geometric relationships.

The Sum Search

Students decompose various polygons into triangles to derive the general formula for the sum of interior angles: (n-2)*180. This transition moves from concrete exploration to algebraic generalization.

Regularity Rules

Focusing on regular polygons, students determine the measures of individual interior and exterior angles. They explore the symmetry and constraints of regularity in geometric design.

Variable Visions

In this synthesis lesson, students use their knowledge of polygon properties to set up and solve multi-step algebraic equations. They model geometric scenarios where side lengths and angles are expressed as variables.