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79 terms

Geometry Formulas and Review

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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)