GRE Geometry

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19 Terms

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Triangle Area

The area of a triangle is calculated using the formula A = 1/2 * base * height, where the base is any side of the triangle and the height is the perpendicular distance from the base to the opposite vertex.

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Isosceles Right Triangle Angles

45,45,90

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Isosceles Right Triangle Side Proportions

(45-45-90) has sides in a ratio of x:x:x√2

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A 30-60-90 triangle has sides in a ratio of

A 30-60-90 triangle has sides in a ratio of x:x√3:2x, with the 1x side opposite the 30 degree angle.

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Pythagorean Theorem

For a right triangle with legs a and b and hypotenuse c: 𝑐2=𝑎2+𝑏2c2=a2+b2. This is called the Pythagorean Theorem

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Right Triangle longest side

A right triangle has a right angle (a 90 degree angle); the side opposite the right angle is called the hypotenuse, and is always the longest side.

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Pythagorean triples

Each side of certain right triangles are integers. These sets of numbers are called Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, 7-24-25. A multiple of a Pythagorean triple is a Pythagorean triple (e.g., 6-8-10)

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Triangle Longest side compared to other two sides

The length of the longest side can never be greater than the sum of the two other sides

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Triangle shortest side compared to other two sides

The length of the shortest side can never be less than the positive difference of the other two sides

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Circle Area

Area=πr2

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Circumference

Circumference=2πr

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Arc

A circle has 360 degrees. An arc is the portion of the circumference of a circle in x degrees of the circle

A fraction of the circumference of a circle is called an arc. To find the degree measure of an arc, look at the central angle

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Arc Length

Arc Length=𝑥/360*2πr

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Area of sector

Area of sector=𝑥/360*π𝑟2

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Chord

A chord is a line segment between two points on a circle. A chord that passes through the middle of the circle is a diameter

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Inscribed angles with the same chord/arc

If two inscribed angles hold the same chord, the two inscribed angles are equal

Inscribed angles holding chords/arcs of equal length are equal.

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Degrees of an inscribed angle holding the diameter

An inscribed angle holding the diameter is a right angle (90 degrees)

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Polygon total degrees formula

180(n − 2)

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Cube formulas

  • Cube volume=𝑠3

  • Cube surface area=6𝑠2