# 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

Transformations

• 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
• 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

Circles

• 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

Probability

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