Geometry SAT combined set

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.

Circle

A set of all points a given distance (radius) from a given point, called the center

Chord

A segment with its endpoints on the circle

Diameter

The longest chord of a circle that always passes through the center

Arc

A continuous portion of between two points on the circle

Semi-circle

An arc that is half a circle, the arc’s endpoints are at the diameter, arc measure is 180°

Minor Arc

An arc that is smaller than semi-circle, the arc measure is less than 180°

Major Arc

An arc that is larger than a semi-circle, the arc measure is greater than 180°

Secant

A line that intersects the circle at exactly two points

Tangent

A line that intersects the circle at exactly one point or touches the circle at 1 point

Sector

An area of circle bounded by two radii and an arc

Tangent Conjecture

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Tangent Segment Conjecture

Tangent segments to a circle from a point outside the circle are congruent.

Internally Tangent Circle

Externally Tangent Circle

Common Internally Tangent Circle

Common Externally Tangent Circle

Central Angle

An angle made up of two radius on the circle’s circumference with its vertex at the circle’s center. The measure of the central angle is equal to the measure of its arc.

Inscribed Angle

An angle made up of two chords with its vertex on the circle’s circumference

Chord Central Angles Conjecture

If two chords in a circle are congruent, then they determine two central angles that are congruent.

Chord Arcs Conjecture

If two chords in a circle are congruent, then their intercepted angles are congruent

Perpendicular to a Chord Conjecture

The perpendicular from the center of a circle to a chord is the bisector of the chord

Chord Distance to Center Conjecture

Two congruent chords in a circle are equidistant from the center of the circle

Perpendicular Bisector of a Chord Conjecture

The perpendicular bisector of a chord passes through the center of a circle

Inscribed Angle Theorem

The measure an inscribed angle is half the measure of its intercepted arc

Angle Formed by a Chord and a Tangent Conjecture

The measure of an angle formed by a chord and a tangent is half the measure of its intercepted arc