Geometry Formulas Flashcards

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Questions and Answers

What is the formula for the area of a triangle?

a = ½bh

What is the formula for the area of a rectangle?

a = bh

What is the formula for the area of a circle?

a = πr²

What is the formula for the circumference of a circle?

<p>c = 2πr or c = πd</p> Signup and view all the answers

What is the Pythagorean theorem?

<p>a² + b² = c²</p> Signup and view all the answers

What is the formula for the perimeter of a rectangle?

<p>p = 2(l + w)</p> Signup and view all the answers

What is the distance formula?

<p>d = √((x₂ - x₁)² + (y₂ - y₁)²)</p> Signup and view all the answers

What is the slope formula?

<p>m = (y₂ - y₁) / (x₂ - x₁)</p> Signup and view all the answers

What is the midpoint formula?

<p>M = [(x₁ + x₂) / 2 , (y₁ + y₂) / 2]</p> Signup and view all the answers

What is the perimeter of a triangle?

<p>p = side 1 + side 2 + side 3</p> Signup and view all the answers

If the slope of a line is a/b, what will be the slope of the perpendicular line?

<p>the opposite reciprocal, namely, -b/a</p> Signup and view all the answers

What is the point-slope form of a line?

<p>(y - y₁) = m(x - x₁)</p> Signup and view all the answers

What is the slope-intercept form of a line?

<p>y = mx + b</p> Signup and view all the answers

What is the equation of a vertical line?

<p>x = x₁</p> Signup and view all the answers

What is the equation of a horizontal line?

<p>y = b</p> Signup and view all the answers

What is a 3-sided polygon called?

<p>Triangle</p> Signup and view all the answers

What is a 4-sided polygon called?

<p>Quadrilateral</p> Signup and view all the answers

What is a 5-sided polygon called?

<p>Pentagon</p> Signup and view all the answers

What is a 6-sided polygon called?

<p>Hexagon</p> Signup and view all the answers

What is a 7-sided polygon called?

<p>Heptagon</p> Signup and view all the answers

What is an 8-sided polygon called?

<p>Octagon</p> Signup and view all the answers

What is a 9-sided polygon called?

<p>Nonagon</p> Signup and view all the answers

What is a 10-sided polygon called?

<p>Decagon</p> Signup and view all the answers

What is a 12-sided polygon called?

<p>Dodecagon</p> Signup and view all the answers

What is an n-sided polygon called?

<p>n-gon</p> Signup and view all the answers

What does Sine represent in trigonometry?

<p>Opposite over Hypotenuse (SOH)</p> Signup and view all the answers

What does Cosine represent in trigonometry?

<p>Adjacent over Hypotenuse (CAH)</p> Signup and view all the answers

What does Tangent represent in trigonometry?

<p>Opposite over Adjacent (TOA)</p> Signup and view all the answers

What is the geometric mean of two numbers?

<p>x = √ab</p> Signup and view all the answers

What is the tool that 'undoes' the sine function?

<p>inverse sine (sin⁻¹)</p> Signup and view all the answers

What is the tool that 'undoes' the cosine function?

<p>inverse cosine (cos⁻¹)</p> Signup and view all the answers

What is the tool that 'undoes' the tangent function?

<p>inverse tangent (tan⁻¹)</p> Signup and view all the answers

What is the Law of Sines?

<p>sin(A)/a = sin(B)/b = sin(C)/c</p> Signup and view all the answers

What is the Law of Cosines?

<p>a² = b² + c² - 2(b)(c)cos(A)</p> Signup and view all the answers

What is the formula for the area of a parallelogram?

<p>A = bh</p> Signup and view all the answers

What is the formula for the area of a trapezoid?

<p>A = [(b₁ + b₂)h] ÷ 2 or A = ½(b₁ + b₂)h</p> Signup and view all the answers

What is the formula for the area of a rhombus?

<p>A = ½d₁d₂</p> Signup and view all the answers

What is the formula for the area of a kite?

<p>A = ½d₁d₂</p> Signup and view all the answers

What is the formula for the volume of a prism?

<p>V = B × h (B = area of base)</p> Signup and view all the answers

What is the formula for the volume of a cylinder?

<p>V = B × h (B = πr²)</p> Signup and view all the answers

What is the formula for the volume of a pyramid?

<p>V = (1/3) B × h (B = area of base)</p> Signup and view all the answers

What is the formula for the volume of a cone?

<p>V = (1/3) B × h (B = πr²)</p> Signup and view all the answers

What is the formula for the surface area of a prism?

<p>SA = 2B + (perimeter × height)</p> Signup and view all the answers

What is the formula for the surface area of a cylinder?

<p>SA = 2B + (circumference × height)</p> Signup and view all the answers

What is the formula for the surface area of a pyramid?

<p>SA = B + ½(perimeter × slant height)</p> Signup and view all the answers

What is the formula for the surface area of a cone?

<p>SA = B + ½(circumference × slant height)</p> Signup and view all the answers

What is the formula for the volume of a sphere?

<p>V = (4/3) πr³</p> Signup and view all the answers

What is the formula for the surface area of a sphere?

<p>SA = 4πr²</p> Signup and view all the answers

What is the formula for the area of a regular polygon?

<p>A = ½aP (a = apothem, P = perimeter)</p> Signup and view all the answers

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Study Notes

Area Formulas

  • Area of a Triangle: ( a = \frac{1}{2}bh )
  • Area of a Rectangle: ( a = bh )
  • Area of a Circle: ( a = \pi r^2 )
  • Area of a Parallelogram: ( A = bh )
  • Area of a Trapezoid: ( A = \frac{(b_1 + b_2)h}{2} ) or ( A = \frac{1}{2}(b_1 + b_2)h )
  • Area of a Rhombus: ( A = \frac{1}{2}d_1d_2 )
  • Area of a Kite: ( A = \frac{1}{2}d_1d_2 )
  • Area of a Regular Polygon: ( A = \frac{1}{2}aP ) (where ( a ) is the apothem and ( P ) is the perimeter)

Perimeter and Circumference

  • Perimeter of a Rectangle: ( p = 2(l + w) )
  • Perimeter of a Triangle: ( p = \text{side 1} + \text{side 2} + \text{side 3} )
  • Circumference of a Circle: ( c = 2\pi r ) or ( c = \pi d )

Volume Formulas

  • Volume of a Prism: ( V = B \times h ) (where ( B ) is the area of the base)
  • Volume of a Cylinder: ( V = B \times h ) (with ( B = \pi r^2 ))
  • Volume of a Pyramid: ( V = \frac{1}{3}B \times h )
  • Volume of a Cone: ( V = \frac{1}{3}B \times h ) (with ( B = \pi r^2 ))
  • Volume of a Sphere: ( V = \frac{4}{3} \pi r^3 )

Surface Area Formulas

  • Surface Area of a Prism: ( SA = 2B + (\text{perimeter} \times \text{height}) )
  • Surface Area of a Cylinder: ( SA = 2B + (\text{circumference} \times \text{height}) )
  • Surface Area of a Pyramid: ( SA = B + \frac{1}{2}(\text{perimeter} \times \text{slant height}) )
  • Surface Area of a Cone: ( SA = B + \frac{1}{2}(\text{circumference} \times \text{slant height}) )
  • Surface Area of a Sphere: ( SA = 4\pi r^2 )

Triangle and Polygon Classification

  • Triangle: A 3-sided polygon
  • Quadrilateral: A 4-sided polygon
  • Pentagon: A 5-sided polygon
  • Hexagon: A 6-sided polygon
  • Heptagon: A 7-sided polygon
  • Octagon: An 8-sided polygon
  • Nonagon: A 9-sided polygon
  • Decagon: A 10-sided polygon
  • Dodecagon: A 12-sided polygon
  • n-gon: An n-sided polygon

Trigonometric Functions

  • Sine (SOH): ( \frac{\text{Opposite}}{\text{Hypotenuse}} )
  • Cosine (CAH): ( \frac{\text{Adjacent}}{\text{Hypotenuse}} )
  • Tangent (TOA): ( \frac{\text{Opposite}}{\text{Adjacent}} )
  • Inverse Sine: ( \sin^{-1} )
  • Inverse Cosine: ( \cos^{-1} )
  • Inverse Tangent: ( \tan^{-1} )

Important Theorems and Formulas

  • Pythagorean Theorem: ( a^2 + b^2 = c^2 )
  • Distance Formula: ( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} )
  • Slope Formula: ( m = \frac{(y_2 - y_1)}{(x_2 - x_1)} )
  • Midpoint Formula: ( M = \left[\frac{(x_1 + x_2)}{2}, \frac{(y_1 + y_2)}{2}\right] )

Line Equations

  • Point-Slope Form of a Line: ( (y - y_1) = m(x - x_1) )
  • Slope-Intercept Form of a Line: ( y = mx + b )
  • Equation of a Vertical Line: ( x = x_1 )
  • Equation of a Horizontal Line: ( y = b )

Laws of Trigonometry

  • Law of Sines: ( \frac{\sin(A)}{a} = \frac{\sin(B)}{b} = \frac{\sin(C)}{c} )
  • Law of Cosines: ( a^2 = b^2 + c^2 - 2bc \cos(A) )

Reciprocal Relationships

  • If slope of a line is ( \frac{a}{b} ), the slope of the perpendicular line is ( \frac{-b}{a} )

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