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40 Cards in this Set
- Front
- Back
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Sides of Similar Triangles |
If two triangles are similar, their corresponding sides are proportional.
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Pythagorean Theorem |
a² + b² = c² |
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Area of a Rectangle |
bh
(Base times height) |
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Perimeter of a Rectangle |
2b + 2h
(2 times the base) plus (2 times the height) |
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Area of a Parallelogram (2 formulas) |
bh = bs sin θ
(base times height) (base times slanted side times sin of the angle of the right triangle formed by drawing in the height)
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Perimeter of a Parallelogram |
2b + 2s
(2 times the base) plus (2 times the slanted side) |
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Area of a Triangle |
½bh
(½ times the base times the height) |
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Perimeter of a Triangle |
a + b + c
(add the sides) |
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Semiperimeter of a Triangle |
½ (a + b + c)
(half of the perimeter) |
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Heron's Formula (Area of a Triangle) |
(s = semiperimeter; a, b, c = sides)
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Area of a Trapezoid |
½ (b1 + b2) h
(the average of the top and bottom times the height) |
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Area of a Circle (2 formulas) |
πr² = ¼πd² |
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Circumference of a Circle (2 formulas) |
2πr = πd |
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In a circle:
c -- = ? d |
π |
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Volume of a Rectangular Solid |
lwh
(length times width times height) |
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Total Surface Area of a Rectangular Solid |
2lw + 2lh + 2wh
(l=length, h=height, w=width) |
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Volume of a Right Circular Cylinder |
πr²h |
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Lateral Surface Area of a Right Circular Cylinder |
2πrh |
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Total Surface Area of a Right Circular Cylinder |
2πr(r+h) |
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Volume of a Right Circular Cone |
⅓πr²h |
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Lateral Surface Area of a Right Circular Cone (2 formulas) |
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Total Surface Area of a Right Circular Cone (2 formulas) |
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Volume of a Sphere (2 formulas) |
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Surface Area of a Sphere (2 formulas) |
4πr² = πd² |
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Surface Area of a Pyramid with Different Side Faces |
(base area)+(lateral area) |
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Surface Area of a Pyramid with Side Faces the Same |
(base area)+½(perimeter)(slant length) |
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Volume of a Pyramid |
⅓(base area)h |
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Surface Area of a Torus |
4π²Rr |
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Volume of a Torus |
2π²Rr² |
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Euler's Formula |
For any convex polyhedron (which includes the platonic solids), the number of faces plus the number of vertices minus the number of edges always equals 2.
F+V-E=2 |
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Schläfli Symbol |
The "s" and "m" values put together inside curly braces {} make what is called the "Schläfli symbol" for polyhedra. * "s" (number of sides each face has, cannot be less than 3), and* "m" (number of faces that meet at a corner, cannot be less than 3). |
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What is the Schläfli Symbol for an octahedron? |
{3,4} |
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What is the Schläfli Symbol for an icosahedron? |
{3,5} |
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What are the five platonic solids? |
Tetrahedron Octahedron Cube Dodecahedron Icosahedron |
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Tetrahedron |
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Octahedron |
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Cube |
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Dodecahedron |
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Icosahedron |
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Golden Rectangle Formula |
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