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 |
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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 |
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midpoint |
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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> |
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