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Cheatography

Geometry Final Cheat Sheet Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Statements

condit­ional
an "if, then" statement (p->q)
converse
switches hypothesis and conclusion (q->p)
bicond­itional
combin­ation of condition and its converse "if and only if""
Law of Detachment
condit­ional, and hypothesis is true, conclusion is true
Law of Syllogism
when one true condit­ional is the same as the hypothesis is another true statement
negation
the negation changes truth value
inverse
negates hypothesis and conclusion
contra­pos­itive
switches hypothesis and negates both

Properties

Equality
addition property
if a=b, then a+c=b+c
subtra­ction property
if a=b, then a-c=b-c
multip­lic­ation property
if a=b, then ac=bc
reflexive property
a=a
transitive property
if a=b, then b=a
substi­tution property
if a=b then b can replace a
Congruence
reflexive property
AB = AB, A = A
symmetric property
if AB = CD, then CD = AB
transitive property
if AB = CD and CD = EF, then AB = EF

Triangles

Congruence
ASA
angle, included side, angle
AAS
angle, angle, non-in­cluded side
SSS
side, side, side
SAS
side, included angle, side
HL
hypote­nuse, leg
CPCTC
after triangles proved congruent
Right Triangles
tangent (tan)
opposi­te/­adj­acent
sine (sin)
opposi­te/­hyp­otenuse
cosine (cos)
adjace­nt/­hyp­otenuse
Special Right Triangles
45-45-90
legs: congruent, hyp: √2(leg)
30-60-90
hyp: 2(short leg) long leg: √3(short leg)
Similarity
AA~
two angles equal
SAS~
ratio of sides is equal, included angle congruent
SSS~
all side ratios equal
Pythag­orean Theorem
a2+b2=c2 (right)
obtuse
c2>a2+b2
acute
c2<a2+b2
Triples
(3,4,5) (5,12,13) (8,15,17)
Other
if, a+b>c
then, three sides form a triangle

Tangent Lines

tangent
line that intersects circle at one point
point of tangency
where circle and tangent intersect
congruent segments
the two segments from one point of tangency
 

Properties of Parallel Lines

transv­ersal
line that intersects two coplanar lines at distinct points
alternate interior angles
opposite side of transv­ersal inside of two lines
same side interior angles
same side of transv­ersal inside of two lines
corres­ponding angles
overlap if overlaid
same side exterior angles
same side of transv­ersal outside of two lines
alternate exterior angles
opposite side of transv­ersal outside of two lines
CONVERSES -> PARALLEL LINES

Formulas

AREA
sector
degrees "­rep­res­ent­ed" x πr2
circle
πr2
triangle
1/2 bh or 1/2 bc(sin A)
trapezoid
1/2h(b1+b2)
kite or rhombus
1/2(d1)(d2)
rectangle
bh
parall­elogram
bh
Length
circum­ference
2πr or πd
arc length
central angle/360 x 2πr
Coordinate Geometry
distance



midpoint



Circles in Triangles

point of concur­rency
point at which 3 or more lines intersect
circum­center
point of concur­rency, (p. bisectors)
circum­scribed circle
through all vertices
incenter
point of concur­rency, (a. bisectors)
inscribed circle
largest contained circle
median of triangle
endpoints: vertex, median
centroid
point of concur­rency, (medians)
altitude
p. segment, vertex to opposite side

Vectors

vector
any quantity with magnitude (size) and direction
resultant vector
a+c = <x1,x2><y1,y2>