Geometry formulas Flashcards
Betweenness of points
AB+BC=AC
AB=AC-BC
BC=AC-AB
Midpoint
(x1+x2 y1+y2)
_______ , ________
2 2
Partitioning a line segment
(nx1+mx2 ny1+my2)
__________ , __________
n+m n+m
Where m does not equal -n
weighted average on a number line
Weighted average on a coordinate plane
w1 + w2 -----------------------------------------------
w1+w2+w3 w1y1+w2y2+w3y3 -------------------------- w1+w2+w3
Find missing endpoint
x=x1+x2 , y= y1+y2
_________ __________
2 2
Distance Fromula
D= Sqrt of (x2-x1)^2 + (y2-y1)^2
Slope
M= y2-y1
———
x2-x1
Equation of a line
Standard: Ax + By= C
Slope Intercept: y=mx + b
Point Slope: y-y1+ m(x-x1)
Sum of exterior angles
360 degrees
One exterior angle
n
Sum of interior angles
180(n-2)
One interior angle
n
45-45-90 triangle
Hypotenuse: x Sqrt(2)
Legs: x
30-60-90 triangle
Short leg: x
Long leg: x Sqrt(3)
Hypotenuse: 2x
SOH-CAH-TOA
Sin A= opposite
————-
Hypotenuse
Cos A= Adjacent
—————
Hypotenuse
Tan A= opposite
————–
adjacent
Law of sines
sin A sin B sin C
——– = ——– = ———
a b c
law of cosines
a^2=b^2 + c^2- 2bc cos A
b^2=a^2 + c^2- 2ac cos B
c^2=b^2 + b^2- 2ab cos C
Radius/ Diameter
r= d/2 d=2r
Area of a circle
Circumference
A= (pi)r^2
C= 2(pi)r C= (pi)d
Arc Length
S= 0/360 times 2(pi)r
Area of a sector
A= 0/360 times (pi)r^2
Equation of a circle
(x-h)^2 + (y-k)^2 = r^2
Completing the square
(b/2)^2
Convert degrees to radians
Convert radians to degrees
Multiply by (pi)/180
Multiply by 180/ (pi)
Arc Length in radians
S= 0r
Inscribed angles
1/2 the measure of the intersected arc
_____________________
1/2 the measure of the central angle
Central Angle measurement
Same as the intercepted arc.
2 times the inscribed angle
Angle outside of circle
m<exterior= greater (arc) -lesser(arc)/ 2
Angle inside of a circle
m<exterior= greater (arc) + lesser(arc) /2
Segments of intersecting chords
a(b) = c(d)
Segments of intersecting secants
x(x+y) = w(w+z)
Segments tangent/ Secant intersecting
x^2 = w=(w+z)
segments of intersecting tangents
a=b
prisms
Volume: V= Bh
Surface Area: SA= Ph + 2B
Cylider
Volume: V=Bh
Surface Area: SA= Ph +2b
Central Angle
360/n
Diagonals, number of
n(n-3)/2
Area of rectangle
A = l x w
Area of a trapezoid
A= b1 + b2
—————- x h
2
Area of a square
A= s^2
Area of a parallelogram
A=bh
Area of a rhombus/ kite
A= d1+d2
———–
2
Area of a regular polygon
A= 1/2 aP
Area of a triangle
A- bh /2
Similar right traingle
Altitude x = Sqrt (ab)
short leg: d= Sqrt (ac)
long leg: e= Sqrt (bc)
Pythagorean Theorem
a^2 + b^2 = c^2
