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?

c = 2πr or c = πd Signup and view all the answers

What is the Pythagorean theorem?

a² + b² = c² Signup and view all the answers

What is the formula for the perimeter of a rectangle?

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

What is the distance formula?

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

What is the slope formula?

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

What is the midpoint formula?

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

What is the perimeter of a triangle?

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

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

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

What is the point-slope form of a line?

(y - y₁) = m(x - x₁) Signup and view all the answers

What is the slope-intercept form of a line?

y = mx + b Signup and view all the answers

What is the equation of a vertical line?

x = x₁ Signup and view all the answers

What is the equation of a horizontal line?

y = b Signup and view all the answers

What is a 3-sided polygon called?

Triangle Signup and view all the answers

What is a 4-sided polygon called?

Quadrilateral Signup and view all the answers

What is a 5-sided polygon called?

Pentagon Signup and view all the answers

What is a 6-sided polygon called?

Hexagon Signup and view all the answers

What is a 7-sided polygon called?

Heptagon Signup and view all the answers

What is an 8-sided polygon called?

Octagon Signup and view all the answers

What is a 9-sided polygon called?

Nonagon Signup and view all the answers

What is a 10-sided polygon called?

Decagon Signup and view all the answers

What is a 12-sided polygon called?

Dodecagon Signup and view all the answers

What is an n-sided polygon called?

n-gon Signup and view all the answers

What does Sine represent in trigonometry?

Opposite over Hypotenuse (SOH) Signup and view all the answers

What does Cosine represent in trigonometry?

Adjacent over Hypotenuse (CAH) Signup and view all the answers

What does Tangent represent in trigonometry?

Opposite over Adjacent (TOA) Signup and view all the answers

What is the geometric mean of two numbers?

x = √ab Signup and view all the answers

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

inverse sine (sin⁻¹) Signup and view all the answers

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

inverse cosine (cos⁻¹) Signup and view all the answers

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

inverse tangent (tan⁻¹) Signup and view all the answers

What is the Law of Sines?

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

What is the Law of Cosines?

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

What is the formula for the area of a parallelogram?

A = bh Signup and view all the answers

What is the formula for the area of a trapezoid?

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

What is the formula for the area of a rhombus?

A = ½d₁d₂ Signup and view all the answers

What is the formula for the area of a kite?

A = ½d₁d₂ Signup and view all the answers

What is the formula for the volume of a prism?

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

What is the formula for the volume of a cylinder?

V = B × h (B = πr²) Signup and view all the answers

What is the formula for the volume of a pyramid?

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

What is the formula for the volume of a cone?

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

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

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

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

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

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

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

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

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

What is the formula for the volume of a sphere?

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

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

SA = 4πr² Signup and view all the answers

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

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

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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Description

Test your knowledge of essential geometry formulas with these flashcards. This quiz covers formulas for area, perimeter, and the Pythagorean theorem. Perfect for students needing a quick review or for anyone looking to solidify their understanding of geometric concepts.