Course Description
Geometry 105 develops formal logical reasoning through the study of classical Euclidean geometry. Students progress from foundational definitions and postulates to triangle congruence, similarity, circle theorems, spatial reasoning, and geometric transformations.
Course Information
- Course Code: MATH 105
- Course Title: Geometry 105
- Department: Mathematics
- Prerequisite: Algebra I or equivalent
- Course Length: 16 Weeks
Learning Outcomes
- Construct formal two-column and paragraph proofs
- Apply triangle congruence and similarity criteria
- Solve right triangle and trigonometric problems
- Analyze circle relationships including arcs, chords, and tangents
- Calculate area, surface area, and volume
- Apply rigid and non-rigid transformations
- Demonstrate deductive reasoning and logical precision
Course Units
Unit 1: Foundations of Geometry
Points, lines, planes, segments, angle relationships, and basic constructions.
Unit 2: Logic and Geometric Reasoning
Conditional statements, converses, biconditionals, and formal proof writing.
Unit 3: Parallel and Perpendicular Lines
Transversal angle relationships, proving lines parallel, and coordinate applications.
Unit 4: Triangle Congruence
SSS, SAS, ASA, AAS, HL, CPCTC, and triangle inequalities.
Unit 5: Properties of Triangles
Medians, altitudes, angle bisectors, perpendicular bisectors, and concurrency points.
Unit 6: Polygons and Quadrilaterals
Interior and exterior angle sums, parallelograms, rectangles, rhombuses, squares, trapezoids, and kites.
Unit 7: Similarity
Similarity criteria, proportional reasoning, and indirect measurement.
Unit 8: Right Triangles and Trigonometry
Pythagorean Theorem, special right triangles, and basic trigonometric ratios.
Unit 9: Area and Volume
Area of polygons and circles; surface area and volume of three-dimensional solids.
Unit 10: Circles
Arcs, inscribed angles, chords, secants, tangents, and sector measures.
Unit 11: Transformations
Translations, reflections, rotations, dilations, symmetry, and composition of transformations.
Unit 12: Advanced Geometric Constructions
Compass-and-straightedge constructions including inscribed polygons, locus constructions, and classical geometric construction problems.
Unit 13: Vectors in the Coordinate Plane
Vector representation, magnitude and direction, vector addition and subtraction, and geometric applications in the coordinate plane.
Unit 14: Truth Tables and Logic Rigor
Logical connectives, truth tables, equivalence, and rigorous deductive structures supporting formal geometric proofs.
Assessment Structure
- Unit Quizzes
- Proof Writing Assessments
- Problem-Solving Exams
- Midterm Examination
- Cumulative Final Examination
Pathway Progression
Geometry 105 prepares students for advanced mathematics including Pre-Calculus, Calculus, Discrete Mathematics, and Linear Algebra.