Unit 1: Foundations of Geometry
Basic building blocks
Points, lines, planes, rays, segments
Midpoint and distance formulas
Angle measure and angle addition postulate

Constructions
Copying segments and angles
Bisectors (segment and angle)
Perpendicular and parallel lines

Reasoning and proof basics
Inductive and deductive reasoning
Conditional statements, converse, inverse, contrapositive
Postulates, theorems, and definitions
Two-column, paragraph, and flowchart proofs
Angle relationships
Vertical, linear pair, complementary, supplementary
Angles formed by a transversal (corresponding, alternate interior/exterior, same-side interior)

Proving lines parallel

Coordinate geometry
Slopes of parallel and perpendicular lines
Equations of lines
Distance from a point to a line
Rigid motions
Translations
ReflectionsRotations

Compositions of transformations

Dilations
Scale factor and center of dilation
Similarity transformations

Symmetry
Line and rotational symmetry
Symmetry of regular polygons

Transformations on the coordinate plane
Triangle basics
Classifying triangles
Triangle Sum and Exterior Angle Theorems

Congruence
Congruence via rigid motions
SSS, SAS, ASA, AAS, HLCPCTC

Isosceles and equilateral triangles
Base angles theorem and its converse

Proofs with congruent triangles
Special segments
Perpendicular bisectors and circumcenter
Angle bisectors and incenter
Medians and centroid
Altitudes and orthocenter

Midsegment theorem

Triangle inequalities
Inequality theorem
Hinge theorem and converse

Indirect proof
Similar figures
Ratios, proportions, scale factor
Similarity via transformations

Triangle similarity criteria
AA, SAS, SSS

Similarity theorems
Triangle Proportionality Theorem
Angle bisector theorem
Parts of similar triangles

Applications
Indirect measurement
Scale drawings and models
Pythagorean Theorem and its converse
Special right triangles (45-45-90, 30-60-90)
Geometric mean and right triangle altitude theorems

Trigonometric ratios
Sine, cosine, tangent
Complementary angle relationship
Inverse trig ratios

Applications
Angles of elevation and depression

Law of Sines and Law of Cosines (in some courses)
Polygon angle sums
Interior and exterior angles
Regular polygons

Parallelograms
Properties and proofs
Rectangles, rhombi, squares

Trapezoids and kites
Midsegment of a trapezoid
Isosceles trapezoid properties

Coordinate proofs
Classifying quadrilaterals on the plane
Proving properties with coordinates
Parts of a circle
Radius, diameter, chord, tangent, secant

Arcs and angles
Central angles and arc measure
Inscribed angles and inscribed polygons
Angles formed by chords, secants, and tangents

Segment relationships
Chord-chord, secant-secant, secant-tangent

Arc length and sector area (with radian introduction)

Equation of a circle
Standard form
Completing the square

Constructions
Inscribed and circumscribed circles
Tangent lines
Area of plane figures
Triangles, quadrilaterals, regular polygons
Composite figures
Area on the coordinate plane

Three-dimensional figures
Prisms, cylinders, pyramids, cones, spheres
Cross sections and solids of revolution

Surface area and volume formulas

Cavalieri’s Principle

Effects of scaling
on perimeter, area, and volume

Modeling
Density and real-world applications
Basic probability
Sample spaces and events
Union, intersection, complement

Conditional probability and independence

Counting methods
Permutations and combinations

Geometric probability