USA Geometry Syllabus

  • Basics Of Geometry

    • Points, lines, and planes
    • Measuring and constructing segments
    • Using midpoint and distance formulas
    • Perimeter and area in the coordinate plane
    • Measuring and constructing angles
    • Describing pairs of angles

    Reasoning and Proofs

    • Conditional statements
    • Inductive and deductive reasoning
    • Postulates and diagrams
    • Algebraic Reasoning
    • Proving statements about segments and angles

    Parallel and Perpendicular Lines

    • Pairs of lines and angles
    • Parallel lines and transversals
    • Proofs with parallel lines
    • Proofs with perpendicular lines
    • Equations of parallel and perpendicular lines


    • Translations
    • Reflections
    • Rotations
    • Congruence and transformations
    • Dilations
    • Similarity and Transformations

    Congruent Triangles

    • Angles of triangles
    • Congruent polygons
    • Proving triangle congruence by SAS
    • Equilateral and isosceles triangles
    • Proving triangle congruence by SSS
    • Proving triangle congruence by ASA and AAS
    • Using congruent triangles
    • Coordinate proofs

    Relationships within Triangles

    • Perpendicular and angle bisectors
    • Bisectors of Triangles
    • Medians and altitudes of triangles
    • The triangle midsegment theorem
    • Indirect proof and inequalities in one triangle
    •  Inequalities in two triangles


    • Polygons and Its angles
    • Polygons continution and quadrilaterals
    • Parallelogram
    • Rectangle
    • Rhombus
    • Square
    • Trapezoid and Kite

    Similarity of Triangles

    • Similarity and SSS Similarity of Triangles
    • SAS, AAA or AA Similarity
    • Perimeters and Area ratios of Similar triangles
    • Medians, Altitudes and Angle bisectors ratios of Similar triangles
    • Proportionality Theorem
    • Angle bisector theorem

    Right Angle and Trigonometry

    • The pythagorean theorem
    • Special right triangles
    • Similar right triangles
    • The tangent ratio
    • The sine and cosine ratio
    • Solving right triangles
    • Law of sines and law of cosines


    • Lines and Segments that intersect Circles
    • Finding arc measures
    • Using Chords
    • Inscribed angles and Polygons
    • Angle relationships in Circles
    • Segment relationships in Circles
    • Circles in the Coordinate plane

    Circumference, Area and Volume

    • Circumference and arc length
    • Areas of circles and sectors
    • Areas of polygons
    • 3D figures
    • Volumes of prisms and Cylinders
    • Volumes of pyramids
    • Surface ares and volumes of cones
    • Surface ares and volumes of spheres


    • Sample spaces and probability
    • Independent and dependent events
    • Two way tables and probability
    • probability of disjoint and overlapping events
    • Permutations and combinations
    • Binomial distributions