Math Semester 2 Final Flashcards
Standard Equation of a Circle
(x - h)² + (y - k)² = r²
Density
D = mass/volume
Arc Area
(Area of sector / πr²) = (measure of arc / 360)
Arc Length
(Arc length / 2πr) = (measure of arc / 360)
Circumference
C = 2πr
Area of a Circle
A = πr²
Prism Volume
V = Bh
(B = area of base)
Cylinder Volume
V= πr²h
Cone Volume
V =1/3 x πr²h
Pyramid Volume
V = 1/3 x Bh
Sphere
V = 4/3 x πr³
Special Right Triangles
45-45-90: legs = x. hypotenuse = x√2
30-60-90:
Leg next to 60 = x
Leg next to 30 = x√3
Hypotenuse = 2x
Geometric Mean: Altitude
CD² = AD x BD
Altitude = part x part of hypotenuse
Geometric Mean: Leg
CB² = DB x AB
Leg = corresponding part x whole
Sine
Sin = opposite/hypotenuse
Cosine
Cos = adjacent/hypotenuse
Tangent
Tan = opposite/adjacent
Two Secants Outside a Circle
m∠1 = 1/2 (mBD - mAC)
EA x EB = EC x ED
Secant and Tangent Outside
mm∠1 = 1/2 (mAD - mAC)
EA² = EC x ED
Intersecting Chords Inside
m∠1 = 1/2 (mAC + mDB)
EA x EB = EC x ED
Volume of a Regular Polygon
V = 1/2a x (n x s)
Trapezoid Area
A = 1/2 (b1 + b2) x h
Sine and cosine add up to _____ degrees.
90
What are the similarity theorems?
SSS and AA
In a quadrilateral inscribed in a circle, opposite angles are…
Supplementary
Measure of an Inscribed Angle Theorem
The measure of an inscribed angle is half the measure of its intercepted arc. Intercepted arc = central angle.
Convert degrees to radians
degree/180 x π = rad
Convert radians to degrees
rad x 180 = degree
To complete the square you add _____ to both sides.
c = (b/2)²
Tangent and Intersected Chord Theorem
If a tangent intersects a circle, the measure of each angle formed is half that of the intercepted arc.
Tangents are perpendicular to the ______ of a circle
Radius/Diameter
Circumscribed Angle Theorem
The measure of a circumscribed angle is equal to 180 minus the central angle.
External Tangent Congruence Theorem
Tangent segments from a common external point are congruent.
