In this course, students will explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. They will establish triangle congruence criteria based on analyses of rigid motion and formal constructions, prove theorems, and solve problems about triangles, quadrilaterals, and other polygons. They will identify criteria for similarity of triangles, and apply similarity in right triangles to understand right triangle trigonometry. Studentsâ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Students will also prove basic theorems about circles, and use a rectangular coordinate system to verify geometric relationships.