Geometry Course Curriculum

Geometry is a fundamental mathematics course that explores the properties and relations of points, lines, surfaces, and solids. This course aims to equip students with a solid understanding of geometric concepts, theorems, and proofs while honing their analytical thinking and problem-solving skills.

Students will delve into various topics, including congruence and similarity, measurement and properties of shapes and figures, the Pythagorean Theorem, geometric transformations, and the principles of Euclidean Geometry. In addition, this course will introduce students to concepts of trigonometry, coordinate geometry, and three-dimensional geometry.

Geometry enhances students’ spatial reasoning ability and understanding of the interconnectedness of mathematical principles. They will learn to think critically, construct logical arguments, and solve complex problems – skills applicable to a wide range of subjects and disciplines.

By the end of the course, students gain a strong foundation in geometry necessary for further study in mathematics and sciences. They develop a deep appreciation for the beauty and universality of geometric principles that exist in the world around us.

Semester 1 (0.5 Credits )

  • Points, Lines, and Planes
  • Measuring Segments
  • Measuring Angles
  • Exploring Angle Pairs
  • Basic Constructions
  • Midpoint and Distance in the Coordinate Plane
  • Perimeter, Area, and Circumference
  • Patterns and Inductive Reasoning
  • Conditional Statements
  • Bi-conditionals and Definitions
  • Deductive Reasoning
  • Reasoning in Algebra and Geometry
  • Proving Angles Congruent
  • Lines and Angles
  • Properties of Parallel Lines
  • Proving Parallel Lines
  • Parallel and Perpendicular Lines
  • Parallel Lines and Triangles
  • Constructing Parallel and Perpendicular Lines
  • Equations of Lines in the Coordinate Plane
  • Slopes of Parallel and Perpendicular Lines
  • Congruent Figures
  • Triangle Congruence by SSS and SAS
  • Triangle Congruence by ASA and AAS
  • Using Corresponding Parts of Congruent Triangles
  • Isosceles and Equilateral Triangles
  • Congruence in Right Triangles
  • Congruence in Overlapping Triangles
  • Midsegments of Triangles
  • Perpendicular and Angle Bisectors
  • Bisectors in Triangles
  • Medians and Altitudes
  • Indirect Proof
  • Inequalities in One Triangle

Semester 2 (0.5 Credits )

  • The Polygon Angle-Sum Theorem
  • Properties of Parallelograms
  • Proving a Quadrilateral is a Parallelogram
  • Properties of Rhombuses, Rectangles, and Squares
  • Conditions for Rhombuses, Rectangles, and Squares
  • Trapezoids and Kites
  • Polygons in the Coordinate Plane
  • Ratios and Proportions
  • Similar Polygons
  • Proving Triangles Similar
  • Similarity in Right Triangles
  • Proportions in Triangles
  • The Pythagorean Theorem
  • Special Right Triangles
  • Trigonometry
  • Angle of Elevation
  • Translations
  • Reflections
  • Rotations
  • Dilations
  • Area of Parallelograms and Triangles
  • Area of Trapezoids, Rhombuses, and Kites
  • Area of Regular Polygons
  • Circles and Arcs
  • Areas of Circles and Sectors
  • Space Figures and Cross Sections
  • Surface Areas of Prisms and Cylinders
  • Surface Area of Pyramids and Cones
  • Volumes of Cylinders and Prisms
  • Volumes of Pyramids and Cones
  • Surface Area and Volumes in a Sphere
  • Tangent Lines
  • Chords and Arcs
  • Inscribed Angles in a Circle
  • Angle Measures and Segments
  • Circles in the Coordinate Plane