Geometry Course Outline

The Geometry course introduces the nature of the proof and the use of deductive and inductive reasoning. Students will learn how to work with theorems and geometric constructions during the course of their study and will cover some of the basics of trigonometry. While Jurgensen and Brown on Geometry is the primary textbook, students will also be studying proofs based on Euclid and many of the chapters will track Euclid’s line of proof and deductive reasoning. This course uses Geometry by R. Jurgensen, R. Brown, and J. Jurgensen.

Semester I

Chapter 1: Points, Lines, Planes, and Angles

  • points, lines, and planes
  • segments, rays, and distance
  • angles
  • postulates and theorems

Chapter 2: Deductive Reasoning

  • if-then statements
  • proving theorems
  • angles and perpendicular lines

Chapter 3: Parallel Lines and Planes

  • properties of parallel lines
  • angles of triangles and polygons
  • inductive reasoning

Chapter 4: Congruent Triangles

  • congruent figures
  • isosceles triangle figures
  • perpendicular bisectors

Chapter 5: Quadrilaterals

  • properties of parallelograms
  • special quadrilaterals
  • trapezoids

Semester II

Chapter 6: Inequalities in Geometry

  • inequalities
  • inverses and contrapositives
  • indirect proof
  • triangle inequalities

Chapter 7: Similiar Polygons

  • rates and proportions
  • similar triangle postulates
  • similar triangles

Chapter 8: Right Triangles

  • The Pythagorean Theorem
  • special right triangles
  • sines, cosines, and tangents

Chapter 13: Coordinate Geometry

  • distance formula
  • slope of a line
  • parallel and perpendicular lines
  • vectors graphing linear equations
  • graphing and writing linear equations

Chapter 9: Circles

  • tangents, arcs, and central angles
  • chords
  • inscribed angles
  • circles and lengths of segments

Chapter 11: Areas of Plane Figures

  • rectangles, parallelograms, triangles, and rhombuses
  • circumferences and areas of circles
  • arc lengths and arcs of sectors

Chapter 12: Areas and Volumes of Solids

  • Areas and volumes of prisms, pyramids, cylinders, and cones
  • Areas and volumes of spheres

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