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

Math: Geometry and Trigonometry syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Math: Geometry and Trigonometry in SAT (Scholastic Assessment Test), not a summary of it.

1. 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. 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. 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. 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

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

24 of 50 cards from the Math: Geometry and Trigonometry deck — real questions with worked 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.

21. 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.

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

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

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

    Add the lengths of all of its sides.

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

    Volume = length x width x height.

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