SAT Math Geometry (COVERS EVERY TOPIC ON SAT GEOMETRY)

This consist of EVERY geometry topic including the common ones to the ones you'd rarely find. I included everything bc I want a 1600 lmao

Perimeter of a Rectangle

P = 2(l + w)

Area of a Rectangle

A = l × w

Perimeter of a Square

P = 4s

Area of a Square

A = s²

Perimeter of a Triangle

P = a + b + c

Area of a Triangle

A = ½ × base × height

Circumference of a Circle

C = 2πr

Area of a Circle

A = πr²

Pythagorean Theorem

a² + b² = c²

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Midpoint Formula

M = ((x₁ + x₂)/2

Area of a Parallelogram

A = base × height

Perimeter of a Parallelogram

P = 2(a + b)

Area of a Trapezoid

A = ½ × (base₁ + base₂) × height

Perimeter of a Trapezoid

P = a + b + c + d

Arc Length Formula

L = (θ/360) × 2πr

Sector Area Formula

A = (θ/360) × πr²

Surface Area of a Cylinder

SA = 2πr² + 2πrh

Volume of a Cylinder

V = πr²h

Surface Area of a Cone

SA = πr² + πrl

Volume of a Cone

V = ⅓πr²h

Surface Area of a Sphere

SA = 4πr²

Volume of a Sphere

V = ⁴⁄₃πr³

Surface Area of a Prism

SA = 2B + Ph

Volume of a Prism

V = Bh

Cross Section of a Cube

Square or Rectangle

Cross Section of a Cylinder

Circle (horizontal) or Rectangle (vertical)

Cross Section of a Cone

Circle or Triangle

SOH-CAH-TOA

sin θ = Opp/Hyp

Law of Sines

(a/sinA) = (b/sinB) = (c/sinC)

Law of Cosines

c² = a² + b² - 2ab cos C

Equation of a Circle

(x - h)² + (y - k)² = r²

Inscribed Angle Theorem

Inscribed angle = ½ of intercepted arc

Reflection Rule across x-axis

(x

Reflection Rule across y-axis

(x

Rotation 90° Counterclockwise

(x

Rotation 180°

(x

Tangent-Chord Theorem

Angle = ½ of intercepted arc

Dilation Formula

(x

Cosine Ratio

cos θ = Adjacent / Hypotenuse

Tangent Ratio

tan θ = Opposite / Adjacent

Reciprocal of Sine

csc θ = 1/sin θ = Hypotenuse / Opposite

Reciprocal of Cosine

sec θ = 1/cos θ = Hypotenuse / Adjacent

Reciprocal of Tangent

cot θ = 1/tan θ = Adjacent / Opposite

Solving Right Triangle Problems

Use SOH-CAH-TOA to find missing sides or angles

Law of Sines

(a/sinA) = (b/sinB) = (c/sinC)

Law of Cosines

c² = a² + b² - 2ab cos C

Basic Trig Identity

sin²θ + cos²θ = 1

Another Trig Identity

tan θ = sin θ / cos θ

Circumscribed Circle

A circle that passes through all vertices of a polygon

Inscribed Circle

A circle that touches all sides of a polygon internally

Transformations

Movement of a shape on the coordinate plane

Translation Rule

(x

Reflection Rule across x-axis

(x

Reflection Rule across y-axis

(x

Rotation 90° Counterclockwise

(x

Rotation 180°

(x

Dilation Formula

(x

Equation of a Circle

(x - h)² + (y - k)² = r²

Finding Circle Center & Radius

From (x - h)² + (y - k)² = r²

Intersection of Two Circles

Solve both circle equations simultaneously

Intersection of a Line & a Circle

Substitute line equation into circle equation & solve

Tangent-Chord Theorem

Angle = ½ of intercepted arc

Chord Perpendicular to Diameter

It bisects the chord

Two Tangents from a Point

They are equal in length

Power of a Point Theorem

PA × PB = PC × PD for chords

Analytical Geometry

Using algebra to solve geometric problems

Finding Distance Between Two Shapes

Use the distance formula or algebraic methods.