GRE Geometry Rules

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Last updated 8:52 PM on 9/27/26
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20 Terms

1
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Area of a triangle

area = ½ base x height

2
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pythagorean theorem

a² + b² = c²

3
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what are the 4 most common Pythagorean triples?

3-4-5
5-12-13
7-24-25
8-15-17

4
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What is the relationship between an angle and a side on a triangle

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5
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what are the sides of a triangle that’s 90, 30 and 60 degrees?

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6
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what are the sides of a triangle that’s 90-45-45 degrees

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7
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third side rule

the third side of a triangle is greater than the difference of the other two sides and less than their sum

(a + b) > c > (b - a)

8
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area of a parallelogram

area = base x height

9
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sum of angles in a polygon

180(n - 2)

n = number of sides

10
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volume of a cylinder

volume = 𝜋r²h

11
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surface area of a cylinder

2𝜋r² + 2𝜋rh

12
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surface area of a box

2lw + 2wh + 2lh

13
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sector area and arc length are proportional to what?

angle size

14
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an inscribed angle is equal to ___ of the arc it intercepts

half

<p>half</p>
15
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what is the diameter of a circle?

2r

16
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what is the circumference of a circle?

𝜋d or 2𝜋r

17
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what is the area of a circle?

𝜋r²

18
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<p>if you have endpoints (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>) of a line on a coordinate plane, what is the midpoint? </p>

if you have endpoints (x1, y1) and (x2, y2) of a line on a coordinate plane, what is the midpoint?

midpoint = ( (x1 + y1)/ 2 , (x2 + y2)/2)

19
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<p>if you have endpoints (x<sub>1</sub>, y<sub>1</sub>) and (x<sub>2</sub>, y<sub>2</sub>) of a line on a coordinate plane, what is the distance? </p>

if you have endpoints (x1, y1) and (x2, y2) of a line on a coordinate plane, what is the distance?

√(x2 - x1)² + (y2 - y1)²

20
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how do you find the slope of an algebraic equation?

slope = rise/run

(y2 - y1) / (x2 - x1)