Honors Geometry Course Syllabus

First Quarter Topics

Unit 1: Tools of Geometry

  • Points, lines, and planes
  • Measuring Segments
  • Measuring and classifying angles
  • Classifying and exploring angle pairs
  • Constructing segments and angles
  • Distance and midpoints in the coordinate plane
  • Area and perimeter of basic geometric figures

Unit 2: Logic and Reasoning

  • Patterns and inductive reasoning
  • Conditional statements
  • Biconditional statements and good definitions
  • Deductive reasoning: Law of detachment and Law of syllogism
  • Negations, inverses, and contrapositives
  • Applying the laws of logic/solving logic problems
  • Reasoning in Algebra and Geometry

Unit 3: Lines and Angles

  • Proving angles are congruent
  • Angles formed by transversals
  • Properties of parallel lines
  • Proving lines are parallel
  • Parallel and perpendicular lines
  • Lines in the coordinate plane (slope-intercept/point-slope form)
  • Slopes of parallel and perpendicular lines
  • Constructing parallel and perpendicular lines
  • Distance between a point and a line

Second Quarter Topics

Unit 4: Congruent Triangles

  • Triangle Sum Theorem/Triangle Exterior Angle Theorem
  • Congruent Figures
  • Proving triangles are congruent using SSS and SAS
  • Proving triangles are congruent by ASA and AAS
  • Using congruent triangles: the CPCTC theorem
  • Isosceles and equilateral triangles
  • Right triangles and the HL theorem
  • Using congruent parts of triangles: CPCTC revisited

Unit 5: Relationships within Triangles

  • Midsegments of triangles
  • Perpendicular and Angle Bisectors
  • Bisectors in triangles
  • Medians and altitudes of triangles
  • Concurrent Lines: orthocenter, incenter, circumcenter, centroid
  • Writing Indirect Proofs
  • Inequalities in one triangle

Unit 6: Quadrilaterals

  • Polygon Sum Theorem
  • Classifying quadrilaterals: the special quadrilateral hierarchy
  • Properties of parallelograms
  • Proving that quadrilaterals are parallelograms
  • Special parallelograms: rhombuses, rectangles, and squares
  • Trapezoids and kites
  • Quadrilaterals in the coordinate plane
  • Writing proofs using coordinate geometry

Third Quarter Topics

Unit 7: Similarity

  • Ratios and proportions
  • Similar polygons
  • Proving triangles are similar
  • Similarity in right triangles
  • The Golden Ratio

Unit 8: Right Triangles and Trigonometry

  • The Pythagorean Theorem and its converse
  • Special right triangles: 30-60-90 right triangle and 45-45-90 right triangle
  • The tangent ratio
  • The sine and cosine ratios
  • Angles of elevation and depression
  • Vectors
  • Law of Sines and Cosines

Unit 10: Area and Perimeter

  • Areas of parallelograms and triangles
  • Areas of trapezoids, rhombuses, and kites
  • Areas of regular polygons
  • Perimeters and areas of similar figures
  • Trigonometry and area
  • Circles and arcs: circumference and arc length
  • Circles and sectors: area and sector area
  • Geometric Probability

Fourth Quarter Topics

Unit 11: Volume and Surface Area

  • 3-D figures and Cross Sections
  • Drawing nets
  • Surface area of prisms and cylinders
  • Surface area of pyramids and cones
  • Volume of prisms and cylinders
  • Volume of pyramids and cones
  • Surface area and volume of spheres
  • Surface area and volume of similar solids

Unit 9: Transformations

  • Translations
  • Reflections
  • Rotations
  • Symmetry
  • Dilations
  • Glide Reflections
  • Applications of Reflections

Unit 12: Circles

  • Tangent lines
  • Chords and arcs
  • Inscribed angles
  • Circles in the coordinate plane