422 Advanced Geometry

2 semesters, 1 credit

Open to sophomores

Prerequisites: Minimum grade of B- in 415 Advanced Algebra I and teacher approval

Advanced Geometry students will study congruent and similar triangles and properties of parallel lines and writing 2-column proofs during first semester. Second semester topics include areas, surface areas, volumes, and basic triangle trigonometry. These are the same topics as 420 Geometry, but in greater depth and at a faster pace. Additional topics include circles, coordinate geometry, more proofs, surface areas, and volumes. A TI-84 graphing calculator is required for this class.


By the completion of this course, students will be able to…

  1. Correctly use the symbols, definitions, properties, postulates, and theorems of geometry in proofs and application problems.
  2. Distinguish between information that may or may not be assumed from geometric diagrams, thereby demonstrating the understanding of using only valid assumptions.
  3. Write deductive proofs based on valid assumptions and deductive logic using definitions, properties, postulates, and theorems.
  4. Apply the geometric concepts of congruence, similarity, parallelism, and equality to application problems. 
  5. Demonstrate their understanding of the attributes of polygons and solids by correctly calculating areas, perimeters, surface areas, and volumes.
  6. Apply their knowledge of ratios to relationships among the parts of a triangle, specifically sine, cosine, and tangent.
  7. Create Geometric diagrams, including triangles, parallel lines cut by a transversal, polygons, and circles.
  8. Find the sine, cosine, and tangent of an angle.
  9. Construct altitudes, medians, and perpendicular bisectors of triangles.
  10. State the properties of quadrilaterals.
  11. Calculate the interior and exterior angles of polygons.
  12. Solve for parts of right triangles and calculate angles of elevation and depression. 


By the completion of this course, students will know…

  1. Basic defined and undefined terms such as distance, angles, congruent segments, congruent angles and types of triangles, conditional statements, postulates, and theorems  
  2. The purpose of a two column proofs 
  3. The principles of parallel lines and planes, perpendicular lines, skew lines, angles formed by two lines cut by a transversal, sum of angles in a triangle, exterior angle of triangle properties, types of polygons, and the sum of interior and exterior angles of polygons
  4. How to prove congruent and similar triangles 
  5. The structure of parallelograms, rectangles, rhombuses, squares, trapezoids, midsegment of triangles, indirect proofs, inequality properties of sides and angles of triangles 
  6. The properties of quadrilaterals  
  7. The purpose of ratios, proportions, similar polygons, and applications involving similar triangles.
  8. Properties of right triangles, special right triangles, basic trigonometric ratios, and applications involving angles of elevation and depression 
  9. Definitions and measures of circles and how to identify parts of a circle 
  10. Perimeters and areas
  11. Surface area and volume 


This course last updated on January 27, 2021, by the Math Department.