for Rising 8th Graders

Click Here to take the free Online TJ Math Diagnostic (email is required).

Many students who apply to TJ are only taking Algebra I in 8th grade, others are only beginning geometry in 8th grade and will have little of the course under their belts when the test is administered in the fall. This puts them at a distinct disadvantage when taking the TJ test.

This crash course in geometry is designed for rising 8th graders who have completed pre-algebra, although pre-algebra isn’t essential to benefit from our course.

This class is not a substitute for a thorough course in geometry. However, a student does not need a thorough course in geometry to handle the geometry problems on the TJ test, SSAT, ISEE, PSAT, and SAT. As long as the student knows some key concepts he or she can solve all the problems that are found on these tests. [It is important to understand that we will NOT be covering proofs. Formal geometric proofs are not needed for these tests.]

The course runs four consecutive days; each class is 90 minutes long. Class size is limited to twelve students. Please allow 2 hours and arrive a few minutes early so we can cover the essentials and answer all of the students’ questions.

We reserve the right to change the pacing of the course to meet the needs of the students. Keep in mind we draw our student pool from across the metro DC area and curriculum varies from school to school, county to county, and public versus private. It is a challenge to both keep the class moving and yet not leave some students behind scratching their heads in confusion.

Class Times 2019

This class is now scheduled for Monday, July 29 through Thursday, August 1 from 6:30pm to 8:30pm.  Please email questions to

Geometry Class Syllabus

Basics of Geometry Patterns and Inductive Reasoning

  • points, lines, planes,
  • angles and their measures
  • segments and their measures
  • angle pair relationships

Intro to Basic Figures

  • perimeter
  • circumference
  • area

Deductive Reasoning and Proof

  • conditional statements
  • If-then statements
  • converses, contrapositive

Perpendicular and Parallel Lines

  • lines and angles
  • proofs and Perpendicular Lines
  • parallel lines and transversals
  • proving lines are parallel
  • using properties of parallel lines
  • parallel lines in the coordinate plane
  • special pairs of angles
  • perpendicular lines

 Properties of Triangles

  • Congruent Triangles
  • triangles and angles
  • congruence and triangles
  • showing triangles are congruent: SSS and SAS
  • showing triangles are congruent: ASA and AAS
  • using congruent triangles
  • isosceles, equilateral, and right triangle
  • perpendiculars and bisectors
  • bisectors of a triangle
  • medians and altitudes of a triangle
  • mid-segment theorem
  • inequalities in one triangle
  • area and perimeter of triangles
  • indirect proof and inequalities in two triangles


  • polygons
  • properties of parallelograms
  • proving quadrilaterals are parallelograms
  • rhombuses, rectangles, and squares
  • trapezoids and kites
  • special quadrilaterals
  • diagonals, perimeter, and area of quadrilaterals


  • ratio and proportion
  • problem solving in geometry with proportions
  • similar polygons
  • similar triangles
  • proving triangles are similar
  • proportions and similar triangles

Right Triangles and Trigonometry

  • similar right triangles
  • pythagorean theorem
  • the converse of the pythagorean theorem
  • special right triangles:30-60-90 & 45-45-90
  • solving right triangles


  • tangent to circles
  • arcs and chords
  • inscribed angles
  • other angle relationships in circles
  • segment lengths in circles
  • equations of circles

Area of Polygons and Circles

  • angle measures in polygons
  • areas of regular polygons
  • perimeters and areas of similar figures
  • circumference and arc length
  • areas of circles and sectors
  • geometric probability

Coordinate Geometry

  • equation of a line
  • parallel lines
  • perpendicular lines
  • reflections
  • y-intercepts
  • x-intercepts


  • reflections
  • rotations
  • translations

This course includes:

  • Daily Quizzes
  • Daily Homework


Caroline Hesse




Contact Kate at 703-203-5796 or and Caroline at 703-870-4280 or