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Geometry and Trigonometry Flashcards

Geometry and Trigonometry covers the spatial reasoning and measurement topics tested on the SAT Math section. This includes properties of triangles and circles, area and volume formulas, coordinate geometry concepts, trigonometric ratios, and special right triangles.

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What is the Pythagorean theorem?

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a^2 + b^2 = c^2, where c is the hypotenuse of a right triangle.

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

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x : x*sqrt(3) : 2x (short leg : long leg : hypotenuse).

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

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x : x : x*sqrt(2) (leg : leg : hypotenuse).

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What is the area formula for a triangle?

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A = (1/2) * base * height.

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What do the interior angles of a triangle sum to?

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180 degrees.

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What is the sum of interior angles of a polygon with n sides?

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(n - 2) * 180 degrees.

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What is the area of a circle?

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A = pi * r^2.

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What is the circumference of a circle?

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C = 2 * pi * r (or pi * d).

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What is the arc length formula for a central angle of theta degrees?

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Arc length = (theta / 360) * 2 * pi * r.

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What is the equation of a circle in standard form?

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(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

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How do you find the midpoint of a segment with endpoints (x1, y1) and (x2, y2)?

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Midpoint = ((x1 + x2)/2, (y1 + y2)/2).

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What is the distance formula between two points?

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d = sqrt((x2 - x1)^2 + (y2 - y1)^2). It's the Pythagorean theorem applied to coordinates.

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What is SOH-CAH-TOA?

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

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What is sin(30 degrees)?

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1/2.

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What is cos(60 degrees)?

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1/2. Note: sin(30) = cos(60) because 30 and 60 are complementary angles.

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What is the volume of a cylinder?

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V = pi * r^2 * h.

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

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V = length * width * height.

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What is the relationship between an inscribed angle and its intercepted arc?

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An inscribed angle is half the measure of its intercepted arc.

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Study Tips for Geometry and Trigonometry

1

Memorize the 30-60-90 and 45-45-90 side ratios cold. The SAT no longer provides a reference sheet, so you must know these from memory.

2

For circle problems, always identify the radius first. Nearly every circle formula (area, circumference, arc length, sector area) depends on r.

3

Practice converting between degrees and radians: 180 degrees = pi radians. The SAT occasionally uses radian measure in trig problems.

4

On coordinate geometry questions, sketch a quick diagram. Visualizing the points and shapes often reveals the fastest solution path.

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