Praxis Geometry study plan

Build a one-page formula sheet covering perimeter, area, surface area, and volume for triangles, quadrilaterals, circles, prisms, cylinders, pyramids, cones, and spheres

Derive each area and volume formula from a diagram rather than memorizing it, and annotate the sheet with the derivation sketch

Solve 25 mixed area and volume problems, including composite figures and solids with a section removed, showing every substitution step

Classify and correct your own errors into categories: formula recall, unit conversion, algebraic slip, misread question

State and apply the angle relationships formed by parallel lines cut by a transversal, and by angle bisectors and perpendicular bisectors

Prove triangle congruence using SSS, SAS, ASA, AAS, and HL, and identify when SSA fails

Apply the triangle inequality, exterior angle theorem, and midsegment theorem to numeric problems

Write two complete two-column or paragraph proofs of your own construction without looking at a model

Prove and apply the properties of parallelograms, rectangles, rhombi, squares, trapezoids, and kites, including diagonal properties

Use the midpoint, distance, and slope formulas together to classify a quadrilateral from its four vertices

Solve coordinate-geometry problems involving parallel and perpendicular lines, including writing equations of lines through given points

Convert fluently between slope-intercept, point-slope, and standard forms of a line

Apply the Pythagorean theorem and its converse, including Pythagorean triples and distance in the coordinate plane

Solve right-triangle problems with 30-60-90 and 45-45-90 special triangles without a calculator

Use sine, cosine, and tangent ratios to find missing sides and angles, and choose the correct inverse function for angle problems

Solve multi-step word problems involving angles of elevation and depression

Compute central angles, arc measures, arc length, and sector area, and distinguish major from minor arcs

Apply the inscribed angle theorem, the tangent-chord angle relationship, and the intersecting chords, secants, and tangents theorems

Solve problems combining circle theorems with the Pythagorean theorem and with similar triangles

Derive the equation of a circle from its center and radius, and complete the square to recover center and radius from general form

Identify and apply similarity criteria AA, SSS, and SAS, and set up correct proportions between corresponding parts

Use the side-splitter theorem, the altitude-to-hypotenuse relationships, and geometric mean in right triangles

Compute scale factors and use them to relate lengths, areas, and volumes of similar solids

Solve dilation problems on the coordinate plane, including negative and fractional scale factors

Perform and describe transformations: translations, reflections, rotations, and dilations, using coordinate rules

Identify line and rotational symmetry of polygons and predict the image of a figure under a composition of transformations

Compute surface area and volume of composite solids and solids of revolution

Convert between cubic and square units and solve density and capacity problems grounded in volume

Take two full-length timed practice tests under exam conditions and score them against the answer key

Re-teach yourself every missed objective using your own notes and formula sheet, then re-solve each missed item from scratch

Drill the highest-frequency weak areas identified by both practice tests until you reach consistent accuracy

Rehearse pacing: budget time per item, flag and skip, and verify answers by substitution or estimation