NY Regents Geometry study plan
NY Regents Geometry · Give each week a clear focus.
8 weeks · About 6 hours per week
Congruence
Write and justify all five congruence criteria (SSS, SAS, ASA, AAS, HL) and state why SSA and AAA fail
Construct formal two-column proofs for triangle congruence, citing definitions, postulates, and theorems at each step
Solve for missing sides, angles, and variables in congruent figures, including overlapping and shared-side diagrams
Identify and correct invalid proof steps, such as assuming what must be proven or misapplying a criterion
Your checkpoint
A 15-problem proof portfolio (10 complete two-column proofs plus 5 error-analysis corrections), scored at 85% or better against a self-made rubric
Congruence
Prove and apply theorems about parallel lines cut by a transversal, including converse reasoning
Prove triangle theorems: exterior angle, isosceles triangle base angles, and midsegment
Use transformations (reflections, rotations, translations) to establish congruence and map one figure onto another
Prove properties of parallelograms and special quadrilaterals using congruent triangles
Your checkpoint
A one-page theorem sheet listing 12+ theorems with a diagram-free statement and a worked proof of each, spot-checked against the Regents reference sheet
Similarity, Right Triangles, and Trigonometry
Establish triangle similarity via AA, SAS~, and SSS~ and write similarity statements with correct vertex correspondence
Set up and solve proportions for missing lengths in similar figures, including nested and overlapping triangles
Apply the side-splitter (triangle proportionality) theorem and its converse
Compute scale factors and use them to relate perimeters, areas, and volumes of similar figures
Your checkpoint
A 12-problem similarity problem set with fully annotated diagrams and proportion setups, plus a written summary of the perimeter/area/volume scale-factor rules
Similarity, Right Triangles, and Trigonometry
Apply the Pythagorean theorem and its converse to classify triangles and find unknown lengths
Use 30-60-90 and 45-45-90 triangle ratios to find exact side lengths without a calculator
Define sine, cosine, and tangent for acute angles and solve right-triangle problems for missing sides and angles
Solve multi-step word problems involving angles of elevation and depression
Your checkpoint
A timed 20-question right-triangle and trigonometry quiz completed in 40 minutes with a score of 80% or higher
Circles
Identify and calculate central angles, inscribed angles, and arcs, applying the inscribed-angle and semicircle theorems
Apply chord, secant, and tangent theorems, including tangent-radius perpendicularity and equal tangent segments
Solve for missing lengths using intersecting chords, secants, and tangent-secant power relationships
Compute arc length and sector area from radius and central angle
Your checkpoint
A circle-theorem flowchart plus 10 solved problems, one per theorem family, each with the governing relationship written before the computation
Expressing Geometric Properties with Equations
Derive and use slope, midpoint, and distance formulas, including partitioning a directed segment in a given ratio
Write and interpret equations of lines parallel and perpendicular to a given line through a specified point
Classify quadrilaterals by coordinates using slope and distance, proving parallel sides, right angles, and congruent sides
Write the equation of a circle in center-radius form and complete the square to find center and radius
Your checkpoint
A coordinate-geometry proof packet: 3 quadrilateral classification proofs and 3 circle-equation problems, each showing all algebraic steps
Geometric Measurement and Dimension & Modeling with Geometry
Compute volume and surface area of prisms, cylinders, pyramids, cones, and spheres, including composite solids
Apply Cavalieri's principle and describe cross-sections of solids
Solve density and modeling problems that require choosing units and interpreting results in context
Convert between two- and three-dimensional representations, including nets and rotations of plane figures
Your checkpoint
A modeling portfolio of 4 real-world problems (packaging, tank capacity, cross-section design, density), each with a labeled diagram, unit analysis, and a justified answer
Congruence & Similarity, Right Triangles, and Trigonometry & Circles & Expressing Geometric Properties with Equations & Geometric Measurement and Dimension & Modeling with Geometry
Complete two full-length timed practice exams under Regents conditions (3 hours each) and log every error by domain
Re-teach the three weakest sub-topics identified in the error log using worked examples
Build a one-page formula and theorem reference from memory and verify it against the official reference sheet
Practice constructed-response writing: show setup, cite reasons, and state final answers with units
Your checkpoint
An error-analysis log covering both practice exams with a targeted remediation plan listing each weak sub-topic, the corrective action, and a re-attempt score of 80% or higher on those items
Milestones
Week 2: Complete 5 mixed congruence proofs cold (no notes) in 50 minutes with at least 4 fully correct, each earning full credit for stated reasons
Week 4: Score 80% or higher on the timed right-triangle and trigonometry quiz, and correctly solve both special-right-triangle items without a calculator
Week 5: Solve 8 of 10 mixed circle problems correctly, correctly choosing the right theorem family for each without prompting
Week 6: Correctly classify 3 of 3 quadrilaterals from coordinates with valid slope and distance justifications, and convert 2 of 2 circle equations to center-radius form
Week 7: Produce all 4 modeling solutions with correct units and at least 3 of 4 fully justified, including one composite-solid volume and one density problem
Week 8: Score 75% or higher on each full-length practice exam and demonstrate improvement of at least 10 percentage points on re-attempted weak items