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SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry Syllabus

The Math: Geometry and Trigonometry syllabus for SAT (Scholastic Assessment Test) in full: 4 chapters, 13 topics and 14 sub-topics, every one listed below, plus 50 Math: Geometry and Trigonometry flashcards with answers.

4Chapters
13Topics
14Sub-topics
50Flashcards

Math: Geometry and Trigonometry syllabus: all 4 chapters

Expand any chapter to see its topics and sub-topics.

  1. Lines, Angles, and Triangles

     4 topics
    • Angle relationships
      • Vertical, complementary, supplementary angles
      • Parallel lines cut by a transversal
    • Triangle properties and theorems
      • Angle sum and exterior angle
      • Similarity and congruence
    • The Pythagorean theorem
      • Common Pythagorean triples
    • Special right triangles
      • 30-60-90 and 45-45-90 triangles

  2. Area, Perimeter, and Volume

     3 topics
    • Area and perimeter of polygons
    • Surface area and volume of solids
      • Prisms, cylinders, cones, spheres
    • Composite figures and reference formulas

  3. Circles

     3 topics
    • Circumference and area
    • Arc length and sector area
      • Central angles in degrees and radians
    • Equation of a circle in the coordinate plane
      • Center-radius form
      • Completing the square to find center and radius

  4. Trigonometry

     3 topics
    • Right-triangle trigonometric ratios
      • Sine, cosine, tangent
      • Solving for sides and angles
    • Cofunction and complementary angle relationships
      • sin(x) = cos(90 - x)
    • Radian measure and the unit circle
      • Converting degrees and radians

SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry flashcards — 50 questions with answers

  1. What is the sum of the measures of the angles on one side of a straight line (a linear pair)?

    180 degrees. Two angles forming a linear pair are supplementary.

  2. What is the relationship between vertical angles formed by two intersecting lines?

    Vertical angles are congruent (equal in measure).

  3. Define complementary angles and supplementary angles.

    Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.

  4. When two parallel lines are cut by a transversal, what is true of corresponding angles and of alternate interior angles?

    Both pairs are congruent. Same-side (co-interior) angles are supplementary, summing to 180 degrees.

  5. What is the sum of the interior angles of any triangle?

    180 degrees.

  6. What is the measure of an exterior angle of a triangle, in terms of the interior angles?

    An exterior angle equals the sum of the two non-adjacent (remote) interior angles.

  7. What is the formula for the sum of the interior angles of a polygon with n sides?

    (n - 2) x 180 degrees.

  8. What is the sum of the exterior angles of any convex polygon, one per vertex?

    360 degrees, regardless of the number of sides.

  9. In a triangle, how do the sides relate to the angles opposite them?

    The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

  10. State the Triangle Inequality Theorem.

    The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

  11. What does it mean for two triangles to be similar, and how do their sides relate?

    Similar triangles have congruent corresponding angles and proportional corresponding sides (same shape, possibly different size).

  12. List three triangle congruence criteria.

    SSS (side-side-side), SAS (side-angle-side), ASA (angle-side-angle); also AAS and HL for right triangles.

  13. State the Pythagorean theorem and when it applies.

    For a right triangle with legs a and b and hypotenuse c: a^2 + b^2 = c^2. It applies only to right triangles.

  14. A right triangle has legs 6 and 8. What is the hypotenuse?

    10, since sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10.

  15. Name two common Pythagorean triples.

    3-4-5 and 5-12-13 (also 8-15-17 and 7-24-25, plus any multiples like 6-8-10).

  16. What are the side ratios of a 45-45-90 triangle?

    1 : 1 : sqrt(2). The legs are equal and the hypotenuse is a leg times sqrt(2).

  17. What are the side ratios of a 30-60-90 triangle?

    1 : sqrt(3) : 2, corresponding to the sides opposite the 30, 60, and 90 degree angles.

  18. In a 30-60-90 triangle the hypotenuse is 10. What are the other two sides?

    The short side (opposite 30) is 5, and the side opposite 60 is 5*sqrt(3).

  19. What is the formula for the area of a triangle?

    Area = (1/2) x base x height.

  20. What is the formula for the area of a parallelogram?

    Area = base x height.

Show the other 30 Math: Geometry and Trigonometry flashcards

  1. What is the formula for the area of a trapezoid?

    Area = (1/2)(b1 + b2) x h, the average of the parallel bases times the height.

  2. What is the formula for the area of a rectangle and its perimeter?

    Area = length x width; Perimeter = 2(length + width).

  3. How do you find the perimeter of any polygon?

    Add the lengths of all of its sides.

  4. What is the volume of a rectangular prism (box)?

    Volume = length x width x height.

  5. What is the volume of a right circular cylinder?

    Volume = pi x r^2 x h (base area times height).

  6. What is the volume of a sphere?

    Volume = (4/3) x pi x r^3.

  7. What is the volume of a right circular cone?

    Volume = (1/3) x pi x r^2 x h.

  8. What is the volume of a pyramid?

    Volume = (1/3) x base area x height.

  9. What is the surface area of a sphere?

    Surface area = 4 x pi x r^2.

  10. What is the surface area of a rectangular prism with dimensions l, w, h?

    SA = 2(lw + lh + wh).

  11. What is the lateral (side) surface area of a cylinder?

    Lateral area = 2 x pi x r x h; total surface area adds the two circular bases: 2*pi*r*h + 2*pi*r^2.

  12. How do you find the area of a composite figure?

    Decompose it into basic shapes, find each area, then add (or subtract for holes/cutouts).

  13. What is the formula for the circumference of a circle?

    Circumference = 2 x pi x r, or equivalently pi x d (where d is the diameter).

  14. What is the formula for the area of a circle?

    Area = pi x r^2.

  15. How is a circle's diameter related to its radius?

    The diameter equals twice the radius: d = 2r.

  16. What is the formula for arc length given a central angle in degrees?

    Arc length = (central angle / 360) x 2*pi*r, the fraction of the circumference.

  17. What is the formula for the area of a sector given a central angle in degrees?

    Sector area = (central angle / 360) x pi*r^2, the fraction of the full circle area.

  18. What is the arc length formula when the central angle is in radians?

    Arc length s = r x theta, where theta is in radians.

  19. What is the sector area formula when the central angle is in radians?

    Sector area = (1/2) x r^2 x theta, where theta is in radians.

  20. What is the standard equation of a circle with center (h, k) and radius r?

    (x - h)^2 + (y - k)^2 = r^2.

  21. A circle has equation (x - 3)^2 + (y + 2)^2 = 25. What are its center and radius?

    Center (3, -2) and radius 5 (since 25 = 5^2).

  22. How do you find a circle's center and radius from a general equation like x^2 + y^2 + Dx + Ey + F = 0?

    Complete the square in x and in y to rewrite it as (x - h)^2 + (y - k)^2 = r^2.

  23. Define the sine, cosine, and tangent ratios for an acute angle in a right triangle (SOH-CAH-TOA).

    sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent.

  24. How is tangent related to sine and cosine?

    tan(theta) = sin(theta) / cos(theta).

  25. State the cofunction relationship between sine and cosine for complementary angles.

    sin(theta) = cos(90 - theta) and cos(theta) = sin(90 - theta); the sine of an angle equals the cosine of its complement.

  26. In a right triangle, if sin(x) = cos(y), what is the relationship between angles x and y?

    They are complementary: x + y = 90 degrees.

  27. What are the exact values of sin, cos, and tan of 30 degrees?

    sin 30 = 1/2, cos 30 = sqrt(3)/2, tan 30 = 1/sqrt(3) = sqrt(3)/3.

  28. What are the exact values of sin, cos, and tan of 45 degrees?

    sin 45 = sqrt(2)/2, cos 45 = sqrt(2)/2, tan 45 = 1.

  29. How do you convert between degrees and radians?

    Multiply degrees by pi/180 to get radians; multiply radians by 180/pi to get degrees. (180 degrees = pi radians.)

  30. What are the radian measures of 90, 180, 270, and 360 degrees?

    pi/2, pi, 3*pi/2, and 2*pi radians respectively.

SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry FAQ

What is in the SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry syllabus?

SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry is split into 4 chapters: Lines, Angles, and Triangles, Area, Perimeter, and Volume, Circles and Trigonometry. Together they contain 13 topics and 14 sub-topics.

How many chapters are in SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry?

4 chapters, containing 13 topics and 14 sub-topics. The largest chapter is Lines, Angles, and Triangles, with 4 topics.

Are there flashcards for SAT (Scholastic Assessment Test) Math: Geometry and Trigonometry?

Yes — a 50-card Math: Geometry and Trigonometry deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.