High School Geometry Fundamentals

High School Geometry Fundamentals is a year-round supplemental course designed for driven students who are currently taking Geometry in school and want more than a passing grade — they want to truly own the material. While school pacing moves fast and tests come and go, this course gives students the dedicated practice space to build deep, durable mastery of the concepts that Precalculus, Trigonometry, standardized tests, and college math will all depend on. Each session sharpens skills across the full geometry landscape: triangle congruence and similarity, coordinate geometry, right triangle trigonometry, circle theorems, transformations, and area, surface area, and volume. Students who invest here don't just survive their Geometry class — they walk into every future math course with a genuine, lasting advantage.

Built for Students Who Are Already in Geometry — and Want to Master It

High School Geometry Fundamentals is a year-round supplemental course for students who are actively studying Geometry in school and want to build real, lasting command of the material. Every unit in Geometry builds on the last, and every future math course — Precalculus, Trigonometry, AP Calculus, the SAT and ACT — pulls directly from the foundations laid here. This course exists to make sure those foundations are genuinely solid, not just test-week solid. The student who enrolls here isn't in trouble; they're being strategic. They understand that passing a unit and truly mastering it are two different things, and they're choosing mastery.

Triangles: Congruence, Similarity, and Problem-Solving

A huge portion of Geometry — and of standardized math testing — lives inside triangle relationships. This course builds deep fluency with all five triangle congruence postulates (SSS, SAS, ASA, AAS, and HL) and the three similarity theorems (AA, SAS, SSS), including when and why each one applies. Students practice using CPCTC (Corresponding Parts of Congruent Triangles are Congruent) to extend proofs beyond the initial congruence statement. On the similarity side, students set up and solve proportions to find unknown side lengths — a skill that pays dividends in Trigonometry and beyond. The Triangle Inequality Theorem and the converse of the Pythagorean Theorem round out the picture, giving students precise tools for classifying triangles and evaluating whether a given set of side lengths can even form a triangle.

Right Triangles and Trigonometry

Right triangle reasoning is the engine of half of high school math. This course drills the Pythagorean theorem from multiple angles — including recognizing Pythagorean triples for speed — and builds thorough mastery of the two special right triangles (45-45-90 and 30-60-90) whose ratios students will need to recall instantly in Precalculus and on the SAT. Trigonometric ratios (sine, cosine, tangent via SOH-CAH-TOA) are practiced both forward (finding missing sides) and backward (using inverse trig to find missing angles), including real-world applications like angles of elevation and depression.

Coordinate Geometry, Angle Relationships, and Transformations

This course also builds strong fluency in the analytic side of Geometry. Students work extensively with the distance formula, midpoint formula, and slope — including the relationships between slopes of parallel and perpendicular lines. Angle relationships receive focused attention: students practice identifying and applying vertical angles, linear pairs, supplementary and complementary pairs, and the full set of angles formed when parallel lines are cut by a transversal (alternate interior, alternate exterior, corresponding). Transformations — translations, rotations, reflections, and dilations — are practiced on the coordinate plane with attention to how each affects a figure's position, orientation, and size.

Circles, Area, Volume, and the Bigger Picture

Rounding out the curriculum, students build mastery of circle theorems (inscribed angles, central angles, chords, tangents, and secants) and the standard equation of a circle in the form (x − h)² + (y − k)² = r². Area, surface area, and volume calculations — for everything from basic polygons to cylinders, cones, pyramids, and spheres — are practiced in both pure and applied contexts. Taken together, this course covers every major domain of the high school Geometry curriculum with the depth and repetition that a busy school year rarely allows. Students leave not just having seen this material, but genuinely owning it — ready for whatever comes next.