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43 Cards in this Set
 Front
 Back
Triangle Sum Conjecture

sum of the three angles equals 180 degrees


The properties of Isosceles triangles

two sides are congruent, base angles are congruent


triangle inequalities

the sum of two sides is greater than the third side


shortcuts to congruent triangles

SSS, SAS, AAS, ASA, SSA,


CPCTC

use it to prove shapes are congruent


Polygon interior sum conjecture

180(n2)


exterior angle sum

720


properties of a parallelagram

opposite sides are congruent and parallel
consecutive angles are supplementary diagonals bisect 

Rectangle properties

all angles are right
opposite sides are congruent and parallel diagonals are congruent and bisect e/o 

Rhombus properties

all sides are congruent
diagonals bisect e/o and the angles 

square properties

all sides are congruent
all 90 degree angles diagonals are congruent, bisect e/o and are angle bisectors 

kite properties

consecutive sides are congruent
nonvertex angles are congruent diagonals bisect the vertex angles diagonal bisec the nonvertex diagonal 

trapezoid properties

parallel bases
consecutive angles are supplementary 

Isos. trapezoid

bases are parallel
other sides are congruent base angles are congruent 

triangle midsegment

midsegment parallel to the third sides, divide triangle into 4 congruent triangles


trapezoid midsegment

midsegment parallel to all bases
average of the bases 

Congruent circles

circles that have the same shape and size


concentric circles

a circle inside other circles


radius

the segment connecting the center to any point of the circle


chord

a segment from one point on a circle to the other not including the center


diameter

a segment containing one point of a circle to the other containing the center


tangent

a line that touches on point on the circle


minor arc

a part of the circle arc that is less a semicircle


major arc

a part of the circle more than a semicircle


semicircle

the arc of a cirle that takes up half of the circle


Chord Properties

two chords congruent the central angles are congruent
two chords are congruent, two arcs are congruent perpendicular from center to chord bisects it two chords are congruent, distance from center is congruent perpendicular of the chord bisects the angle; 

Tangent Properties

the radius that intersects a tangent is perpendicular
two tangents that intersect at a point are congruent can be internally and externally tangent to e/o circles can have up to four tangents external and internal 

arc and angle relationships

Inscribed angle is half the measure of the arc
Two or more inscribed angles that are intercepting the same arc are congruent Angles inscribed in semicircle are 90 degrees 

circumference vs area

Circumference divided by diameter equals pi
Area= pi r^2 

The Pythagorean Theorem

a^2 + b^2 = c^2


Pythagorean Theorem triples

nice numbers that work in the Pythagorean theorem


454590

a= a
b= a c= a sq. rt. 2 

306090

a= a
b= a sq. rt. 3 c= 2a 

Distance equation

sqroot(x1x2)^2 + (y1 + y2)^2


Simularity shortcuts

AA
SAS SSS 

Geometric means

a/x= c/a
b/y= c/b h/x= y/h 

porportional parts

abc is simular to def
ab/de= bc/ef = ca/fd 

scale factor in terms of...

sf
area (sf)^2 surface area(sf)^2 volume (sf)^3 mass(sf)^3 

area
Prism Sphere Cone Pyramid Cylinder 
Prism base times height
Sphere 4/3 pi r^3 Cone 1/3 pi r^2 times height Pyramid 1/3 bh Cylinder bh 

Centroid

medians


Incenter

angle bisectors


circumcenter

perpendicular bisectors


orthocenter

altitudes
