Ohio OST Geometry study plan

Define and apply the foundational vocabulary of transformations, congruence, and similarity, writing precise definitions for rigid motions, congruence, and similarity in your own words.

Perform and describe single and composite rigid motions (translations, rotations, reflections) on the coordinate plane, including sequences that map one figure onto another.

Construct and justify congruence proofs using triangle congruence criteria (SSS, SAS, ASA, AAS, HL) and identify when SSA does not guarantee congruence.

Explain how transformations establish congruence and similarity formally rather than by measurement alone.

Apply dilations centered at a point, including on and off the origin, to produce similar figures and compute scale factors.

Prove triangles similar using AA, SSS similarity, and SAS similarity, and use similarity to solve for unknown lengths.

Derive and use the triangle proportionality theorem and its converse to find segment lengths in triangles cut by parallel lines.

Connect similarity to slope by explaining why the slope of a line is constant using similar right triangles.

Prove and apply the triangle angle sum theorem, exterior angle theorem, and isosceles triangle base-angle theorem.

Prove and use properties of parallelograms and special quadrilaterals, including diagonal properties, to classify figures.

Construct formal two-column or paragraph proofs involving parallel lines cut by a transversal and the resulting angle relationships.

Distinguish between a theorem, a postulate, and a definition, and use each correctly in proof writing.

Derive the equation of a circle from the Pythagorean theorem and use it to identify center and radius.

Complete the square to convert general circle equations into standard form and graph them.

Derive and apply the distance and midpoint formulas, including partitioning a segment in a given ratio.

Use coordinates to prove simple geometric theorems algebraically, such as proving a quadrilateral is a parallelogram or a rectangle.

Apply the Pythagorean theorem and its converse, including identifying Pythagorean triples and classifying triangles by side lengths.

Derive and use the 30-60-90 and 45-45-90 special right triangle ratios to find exact side lengths.

Define sine, cosine, and tangent in right triangles and use them to solve for missing sides and angles.

Solve real-world right-triangle problems involving angles of elevation and depression, drawing accurate diagrams first.

Apply the law of sines and law of cosines to non-right triangles, including the ambiguous case of SSA.

Compute the area of a triangle using the sine formula and solve problems requiring area of composite figures.

Convert between degrees and radians and compute arc length and sector area in circles.

Use the relationship between central angles, inscribed angles, and arcs to find unknown measures.

Compute circumference, arc length, area of circles, sectors, and segments, and solve problems involving composite two-dimensional figures.

Apply volume formulas for prisms, cylinders, pyramids, cones, and spheres, and use volume relationships among similar solids.

Compute surface area of three-dimensional solids, including solids of revolution and composite solids.

Describe cross-sections of three-dimensional objects and identify the solid produced by rotating a two-dimensional figure about an axis.

Synthesize all geometry strands by completing a full-length practice test under timed conditions and recording per-strand accuracy.

Diagnose the three weakest subskills from practice-test data and re-teach each using worked examples.

Write a condensed one-page master reference sheet from memory, then verify and correct it against notes.

Build a final-week review schedule that prioritizes the lowest-accuracy strands.