Middle School Math - Curriculum Guidelines
for Geometry
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Content
Outline/Topics
- Language and Tools of Logic
- If…then statements
- Conditional, Converse, Inverse, Contrapositive
- Logical Equivalence
- Venn Diagrams
- Simple Logic Rules
- Logic Proofs (two column form)
- Point, Line, Plane, Angle
- Postulates
- Existence and Uniqueness
- Collinearity
- Segments
- Rays
- Distance
- Angle Measurement
- Midpoint
- Perpendicularity
- Parallelism
- Transversals
- Special Angles
- If and only if Statements
- Formal Two Column Proofs Using Postulates and Theorems
- Triangle Angle Sum
- Polygons
- Congruent Triangles
- Congruence as a Concept (Size and Shape)
- ASA, SAS, SSS
- Isosceles Triangle Theorems
- AAS, HL
- Altitudes, Medians, Angle Bisectors, Perpendicular Bisectors
- Concurrence & Locus
- Proofs Involving More Than One Pair of Congruent Figures
- Quadrilaterals
- Parallelograms
- Rhombus, Rectangle, Square
- Trapezoids
- Indirect Proofs
- Inequalities
- Similarity
- Congruence vs. Similarity
- Ratio and Proportion
- Similar Polygons
- AA, SAS, SSS Similarity
- Triangle Similarity Theorems
- Right Triangles
- Geometric Means
- Pythagorean Theorem & Its Converse
- Pythagorean Triples
- Classifying Triangles
- Special Right Triangles
- Basic Trigonometric Ratios
- Angles of Elevation & Depression
- Law of Sines
- Circles
- Locus Review
- Basic Terms
- Arcs
- Tangents & Secants
- Central Angles
- Inscribed Angles
- Angles formed by Chords, Tangents, and Secants
- Power Theorems
- Constructions & Loci
- Compass & Straightedge
- The Meaning of Construction
- Perpendiculars & Parallels
- Concurrence Review
- Circle Constructions
- Circumcenter & Incenter
- The Meaning of Locus
- Locus & Construction
- Area
- Area Postulates
- Rectangle Area
- Area of Parallelogram, Triangle, Trapezoid
- Area of Regular Polygons
- Special Area Formulas (Equilateral Triangle, Rhombus, Kite)
- Circle Area & Circumference
- Arc Length & Sector Area
- Area of Similar Figures
- Volume
- Prisms
- Pyramids
- Cylinders & Cones
- Spheres
- Areas & Volumes of Similar Solids
- Coordinate Geometry
- Distance Formula
- Slope
- Midpoint
- Circles
- Parallel & Perpendicular Lines
- Equation of a Line
- Coordinate Geometry Proofs
Extensions/tools:
- Non-Euclidean Geometries (Spherical, etc.)
- Tessellations
- Transformations
- Vectors
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