Standard
Geometry · High school · Math
Topics typically covered
Typical US high school Geometry — aligned with Khan Academy High school geometry units and Common Core Geometry conceptual categories.
Foundations and proof
- Points, lines, and planes — Use undefined terms and basic postulates to describe geometric figures.
- Segments and angles — Apply segment and angle addition; classify angle relationships.
- Reasoning and proof — Write informal and two-column proofs using definitions, postulates, and theorems.
- Parallel and perpendicular lines — Use angle relationships formed by transversals; prove lines parallel.
Transformations
- Translations, rotations, and reflections — Perform rigid motions on the plane and describe them with coordinates.
- Congruence via rigid motions — Explain congruence as the image of a figure under a sequence of rigid motions.
- Dilations — Perform dilations and relate scale factor to corresponding lengths.
Congruence
- Triangle congruence criteria — Apply SSS, SAS, ASA, AAS, and HL to prove triangles congruent.
- Corresponding parts — Use congruence to justify equal corresponding sides and angles.
- Isosceles and equilateral triangles — Apply base angles and related theorems.
Similarity
- Similar polygons — Identify similar figures and write similarity statements and proportions.
- Triangle similarity — Apply AA and related criteria; use proportions in similar triangles.
- Indirect measurement — Use similarity to find inaccessible heights and distances.
Right triangles and trigonometry
- Pythagorean theorem — Solve for missing sides and apply the converse of the Pythagorean theorem.
- Special right triangles — Use 30-60-90 and 45-45-90 side ratios.
- Trigonometric ratios — Define sine, cosine, and tangent in right triangles and solve for sides and angles.
- Right-triangle applications — Solve elevation/depression and other application problems.
Circles
- Parts of a circle — Work with radii, chords, diameters, arcs, and central and inscribed angles.
- Equations of circles — Write and graph circle equations in the coordinate plane.
- Arc length and sector area — Compute arc length and area of sectors.
Coordinate geometry
- Distance and midpoint — Use distance and midpoint formulas on the coordinate plane.
- Parallel and perpendicular slopes — Determine relationships between lines from slopes.
- Coordinate proofs — Prove geometric properties using coordinates.
Area, surface area, and volume
- Area of polygons — Find areas of triangles, parallelograms, trapezoids, and regular polygons.
- Surface area — Find surface area of prisms, cylinders, pyramids, and cones.
- Volume — Find volumes of prisms, cylinders, pyramids, cones, and spheres; apply Cavalieri’s principle informally.
Related courses
Parallel materials covering overlapping topics — not the same as this course page.
- 10th Grade (Common Core)
Grade-level Common Core standards for the same band
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