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Volume of a triangular prism

Bh

Lateral Area of a triangular prism

hp

Surface area of a triangular prism

LA+2B

Volume of a sphere

4/3(pi)r^2

Surface area of a sphere

4(pi)r^2

Arc length

x/360(2[pi]r)

Central angle of a regular polygon

360/n

Area of a sector

x/360(pi)(r^2)

Conditional statement

if p, then q

Converse

if q, then p

Inverse

if not p, then not q

Contrapositive

if not q, then not p

ratio for scale factors and for perimeters

a/b

ratio of areas

(a/b)^2

The SUM of the measures of the INTERIOR angles of a CONVEX n-gon

(n-2)(180)

The measure of EACH INTERIOR angle of a REGULAR n-gon

[(n-2)(180)]/n

An angle whose vertex is on a circle and whose sides contain chords of the circle

Inscribed Angle

In the same circle (or in congruent circles), two chords are congruent if and only if...

They are equidistant from the center

Pythagorean Theorem

(In a right triangle) a^2+b^2=c^2

Hypotenuse of a 30,60,90 triangle

shorter leg x 2

Longer leg of 30,60,90 traingle

shorter leg x square root of 3

Shorter leg of a 30,60,90 triangle

hypotenuse/2

Hypotenuse of a 45,45,90 triangle

leg x square root of 2

Perimeter

Distance around the outside (add all sides)

Circumference of a circle

2(pi)(r) or pi X d

Skew lines

lines that don't intersect and aren't coplanar

Standard equation of a circle

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

If one chord is a perpendicular bisector of another chord, then....

the first chord is a diameter

Volume of a cylinder

(pi)(r^2)(h)

Surface area of a cylinder

[2(pi)(r)(h)] + [2(pi)(r^2)]

Pythagorean triple examples

3,4,5; 5,12,13; 8,15,17

Slope formula

rise/run: (y1-y2)/(x1-x2)

Slopes of parallel lines are....

equal

Perpendicular lines have______ slopes

negative reciprocal

A segment with endpoints on the circle

chord

If an angle is inscribed in a circle, then its measure is....

1/2 the measure of its intercepted arc

A line that intersects a circle in two points

secant

Lateral area of a cylinder

2(pi)(r)(h)

The AREA of a REGULAR n-gon

(1/2)(a)(p)

The measure of EACH EXTERIOR angle of a REGULAR n-gon

360/n

If two segments from the same exterior point are tangent to a circle, then.....

they are congruent

In the same circle (or in cngruent circles), two minor arcs are congruent if and only if....

their corresponding chords are congruent

If a diameter of a circle is perpendicular to a chord, then......

the diameter bisects the chord and its arc

If two inscribed angles of a circle intercept the same arc, then....

the angles are congruent

A quadrilateral can be inscribed in a circle if and only if....

its opposite angles are supplementary

If a tangent and a chord intersect at a point on a circle, then....

the measure of each angle formed is 1/2 the measure of its intercepted arc

Volume of a square pyramid

(1/3)Bh

Lateral area of a square pyramid

(1/2)(L)(p)

Surface area of a square pyramid

LA + B

Area of a triangle

(1/2)bh

Area of a parallelogram

bh

Area of a rectangle

bh; lw

Area of a square

bh; s^2

Area of a trapeziod

(1/2)(h)(b1 + b2)

Area of a circle

(pi)(r^2)

If a line is tangent to a circle, then its perpendicular to....

the radius that drawn to the point of tangency

A line or segment that is tangent to two coplanar circle

common tangent

Coplanar circles that intersect in one point

Tangent circles

Volume of a rectangular solid

lwh

SIN (only in a RIGHT triangle)

opposite/hypotenuse

COS (only in a RIGHT triangle)

adjacent/hypotenuse

TAN (only in a RIGHT triangle)

opposite/ adjacent

Distance Formula

square root of: [(x1-x2)^2 + (y1 - y2)^2]

Midpoint formula

(avg. X, avg. Y): { [(x1+x2)/2], [(y1+y2)/2] }

Coplanar circles that have a common center

Concentric circles

Dodecahedron

12 faces

Icosahedron

20 faces

Algebra rule to rotate 90degrees

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

Algebra rule to rotate 180degrees

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

Algebra rule to rotate 270degrees

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

Algebra rule to reflect over x-axis

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

Algebra rule to reflect over y-axis

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

Algebra rule to reflect over y=x

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

Algebra rule to reflect over y=-x

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

Maximum area formula

(p/4)^2

Measure of an angle with a vertex in the center of a circle

measure of its arc

Measure of an angle with a vertex on the circle

1/2 measure of its arc

Measure of an angle with a vertex inside the circle

1/2 (sum of the arcs)

Measure of an angle with a vertex outside the circle

1/2 (difference of the arcs)