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43 Cards in this Set

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  • 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(n-2)
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
45-45-90
a= a
b= a
c= a sq. rt. 2
30-60-90
a= a
b= a sq. rt. 3
c= 2a
Distance equation
sqroot(x1-x2)^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