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Master SAT Geometry and Trigonometry

Solve SAT area, volume, triangle, trigonometry, circle, and coordinate-geometry questions with efficient visual reasoning.

  • 18 interactive lessons
  • Step-by-step worked examples
  • SAT-style practice questions
Start Lesson 1Browse all lessons

Beginner

  1. Lesson 10%Find perimeter and area of plane figuresChoose and use perimeter, circumference, and area formulas for familiar SAT plane figures, including missing-dimension questions.31 min · 3 practice problems
  2. Lesson 50%Use line and angle relationshipsRecognize vertical angles, linear pairs, and parallel-line angle families, then turn a diagram into an equation for an unknown angle.28 min · 3 practice problems
  3. Lesson 90%Apply the Pythagorean theoremRecognize the hypotenuse, find missing sides, uncover right triangles in diagonals and coordinates, and report exact or rounded distances in the form the SAT asks for.32 min · 3 practice problems
  4. Lesson 160%Read and write circle equationsRead a circle’s center and radius from standard form, write its equation, classify points, and connect equation changes to graph changes.27 min · 4 practice problems

Intermediate

  1. Lesson 20%Break down composite and shaded figuresDecompose SAT composite and shaded figures into familiar regions, then add or subtract areas and related lengths with correct units and exactness.27 min · 3 practice problems
  2. Lesson 30%Find surface area and volumeChoose and use SAT formulas for familiar solids, construct pyramid face slant heights, recover missing dimensions, and combine solid parts.34 min · 4 practice problems
  3. Lesson 40%Use scale factors in two and three dimensionsUse a linear scale factor to predict changes in perimeter, area, surface area, and volume, and recover the linear factor from an area or volume ratio.27 min · 3 practice problems
  4. Lesson 60%Use triangle angle theoremsUse triangle sums, exterior angles, equal-side facts, and polygon decomposition to write an equation for the angle a question asks for.28 min · 3 practice problems
  5. Lesson 70%Solve similar-triangle proportionsMatch corresponding vertices in similar triangles, establish AA from a figure, and use one scale factor to find a missing length or unchanged angle.30 min · 3 practice problems
  6. Lesson 80%Reason with congruence and sufficient informationDecide whether side and angle conditions establish triangle congruence or similarity, then use the resulting correspondence.30 min · 3 practice problems
  7. Lesson 100%Recognize special right trianglesRecognize 45-45-90 and 30-60-90 structures, name the short leg, long leg, and hypotenuse, and scale exact side ratios on the SAT.26 min · 3 practice problems
  8. Lesson 110%Use sine, cosine, and tangentChoose sine, cosine, or tangent from side roles, solve right triangles, use complementary-angle relationships, and interpret signed coordinate ratios.30 min · 3 practice problems
  9. Lesson 140%Use central, inscribed, and tangent anglesIdentify the circle relationship that governs a diagram, then use angles, arcs, tangents, or a bisected chord to find an unknown measure.30 min · 3 practice problems
  10. Lesson 150%Find arc length, sector area, and radian measureUse a central angle as a fraction of a circle to find arc length, sector area, convert angle units, and position radian angles.28 min · 3 practice problems
  11. Lesson 170%Complete the square for a circleChoose between graphing an expanded circle equation and completing the square to find its center, radius, diameter, graph, or exact standard form.28 min · 3 practice problems
  12. Lesson 180%Build circles from coordinate informationTurn diameter endpoints, distance, tangency, and coordinate constraints into circle centers, radii, exact relationships, and standard-form equations.33 min · 3 practice problems

Advanced

  1. Lesson 120%Solve right-triangle inradius problemsUse equal tangent segments to understand the right-triangle inradius formula, then combine it with a given side relationship to find a side, radius, or perimeter.24 min · 3 practice problems
  2. Lesson 130%Use similarity inside right trianglesRecognize the three similar triangles created by an altitude to a right triangle’s hypotenuse, then use geometric-mean proportions to find lengths and work through harder questions.28 min · 3 practice problems