Geometry

Students perform compass-and-straightedge constructions, define rigid motions (reflections, translations, rotations) without reference to a coordinate grid, describe symmetries, and use transformations to prove theorems about lines, angles, and parallel lines.

Students prove that figures are congruent by reasoning about rigid transformations. They prove the Triangle Congruence Theorems (SSS, SAS, ASA), the Perpendicular Bisector Theorem, and several theorems about quadrilaterals.

Students extend rigid transformations to include dilations and define similar figures. They prove the Angle-Angle Triangle Similarity Theorem, use similar right triangles to prove the Pythagorean Theorem and its converse, and use similarity to solve problems.

Students build an understanding of ratios in right triangles, naming cosine, sine, and tangent as trigonometric ratios. They use trigonometry to find missing side lengths and angle measures and apply trigonometry to solve problems in context.

Students practice spatial visualization in three dimensions. They sketch cross-sections, study how surface area and volume scale under dilation, derive volume formulas for prisms, cylinders, pyramids, and cones using Cavalieri’s Principle, and apply their understandings to solve problems.

Students bring algebra and geometry together by working with transformations as functions, equations of circles and parabolas, equations of lines (parallel and perpendicular), coordinate proofs of geometric theorems, and weighted averages.

Students investigate the geometry of circles, including chords, arcs, central and inscribed angles, tangents, cyclic quadrilaterals, inscribed and circumscribed circles of triangles, sector area, arc length, and radian measure.

Students extend their understanding of probability to compound events. They use lists, tables, trees, and Venn diagrams to represent sample spaces, apply the Addition Rule and the Multiplication Rule, define conditional probability, and use probability to test events for independence.