Geometry

Area of a square

s²

Area of a triangle

1/2bh

Area of a rectangle

lw

Area of a regular polygon

1/2aP

Area of a circle

πr²

Area of a parallelogram

Bh

Area of a kite

d1*d2/2

Area of a rhombus

d1*d2/2

Area of an isosceles trapezoid

(b1+b2)/2*h

Circumference of a circle

2πr or πd

Distance Formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

Midpoint Formula

(x₁+x₂)/2, (y₁+y₂)/2

Pythagorean Theorem

a^2+b^2=c^2

Equation of a circle - standard form

(x-h)^2+(y-k)^2=r^2

Triangle Midsegment Theorem

The mid segment is parallel to the base and connects on midpoints on the legs of the triangle and is half the length of the base

Trapezoid Midsegment Theorem

The midsegment of a trapezoid is 1/2 of the sum of the bases

Central angles of a circle

The measure of a central angle is equal to the measure of the intercepted arc

What is the relationship between the measure of an inscribed angle and the intercepted arc?

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

What type of angle is formed by an angle inscribed in a semicircle?

An angle inscribed in a semicircle must be a right angle.

What can be said about inscribed angles that intercept the same arc?

Inscribed angles that intercept the same arc are congruent.

What can be said about inscribed angles that intercept congruent arcs?

Inscribed angles that intercept congruent arcs are congruent.

What do parallel chords intercept?

Parallel chords intercept congruent arcs.

What do congruent chords intercept?

-Congruent chords intercept congruent arcs

Congruent chords are equidistant from what?

Congruent chords are equidistant to the center of the circle

Perpendicular bisectors of chords

A perpendicular bisector of a chord must go through the center of the circle

What is the relationship between a tangent line and a radius at the point of tangency?

A tangent line and a radius are perpendicular.

What can be said about tangent segments from the same external point?

Tangent segments from the same external point are congruent.

How is the angle formed by a chord and a tangent line at the point of tangency related to the intercepted arc?

An angle formed by a chord and tangent line at the point of tangency is half the measure of the intercepted arc.

What is the measure of an angle formed by two lines that intersect inside a circle?

The average of the measure of the intercepted arcs. x=(y+z)/2

What is the measure of an angle formed by two lines that intersect outside of a circle?

Half the difference of the intercepted arcs. x=(z-y)/2

What is the relationship between the segments of two intersecting chords?

The product of the measures of the segments of one chord is equal to the product of the measures of the segments of the other. (ab = cd)

What is the relationship between two secant segments drawn from an external point to a circle?

The product of the lengths of one secant segment and its external segment is equal to the product of the lengths of the other secant segment and its external segment. (a(a+b) = c(c+d))

What is the relationship between a tangent and a secant drawn from an external point to a circle?

The square of the length of the tangent segment is equal to the product of the length of the secant segment and its external segment. (a^2 = b(b+c))

Polygon Exterior Angle Sum Theorem

The sum of the exterior angle measures is 360

Polygon Interior Angle Theorem

(n-2)180

Value of exterior angles in a polygon

360/n

Law of Sines

sinA/a=sinB/b=sinC/c

Law of Cosines

C²=a²+b²-2abcosC

SOHCAHTOA

SIN (Opposite/Hypotenuse) COS (Adjacent/Hypotenuse) TAN (Opposite/Adjacent)

Reflection over the x-axis

(x,y) -> (x,-y)

Reflection over the y-axis

(x,y) -> (-x,y)

Reflection over the line y=x

(x,y) -> (y,x)

Reflection through the origin

(x,y) -> (-x,-y)

Translations

(x,y) -> (x+-h, y+-k) where h and k are the horizontal and vertical shifts respectively

Dialations

(x,y) -> (cx, cy)

Rotation 90 degrees counterclockwise or 270 degrees clockwise

(x,y) -> (-y,x)

Rotation 180 degrees counterclockwise or clockwise

(x,y) -> (-x,-y)

Rotation 270 degrees counterclockwise or 90 degrees clockwise

(x,y) -> (y,-x)

30-60-90 triangle

x, x√3, 2x

45-45-90 triangle

x, x, x√2

Volume of Prisms/Cylinders

Bh where B is the area of the base and h is the height of the prism or cylinder.

Surface Area of Prisms/Cylinders

2B+ph where B is the area of the base, p is the perimeter of the base, and h is the height of the prism or cylinder.

Volume of Pyramids/Cones

1/3Bh where B is the area of the base and h is the height of the pyramid or cone.

Surface Area of Pyramids/Cones

B+1/2pl where B is the area of the base and l is the slant height of the pyramid or cone.

Volume of Spheres

4/3πr³ where r is the radius.

Surface Area of Spheres

4πr²