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Collinear
Points on the same line
Coplaner
points on the same plane
Non collinear
points not on the same line
non coplaner
points not on the same plane
area of a Rectangle
Base
x height
area of a triangle
Base x height / 2
b
x h / 2
Area of a parallelagram
Base x Height
Area of a circle
A= Pi(r
^{2)}
^{ }
Circumference of a circle
C= Pi (d)
D= diameter
diameter of a circle
D=2r
r=Radius
Complementary angle is equal to :
90 degrees
Supplementary angle is equal to :
180 degrees
Midpoint formula
M = (X
_{1 }
+ X
_{2 }
/ 2 , Y
_{1}
+ Y
_{2 }
/ 2)
_{ }
Endpoint formula
( X
_{1}
+ X / 2 = X
_{2 }
_{ , }
Y
_{1}
+ Y / 2 = Y
_{2 }
)
Distance Formula
D = [ ( x
_{1}
-x
_{2 }
)
^{2 }
+ ( y
_{1}
-y
_{2 }
)
^{2}
[ = square root sign
^{ }
Linear pair
Two angles that create a line
Theorem: All verticle angles are....
Congruent
Acute angle
Less than 90 degrees
Obtuse angle
More than 90 degrees
Straight angle
180 degrees
To bisect an angle is to
cut it in half
Adjacent angles are
next to eachother. no overlapping
Conditional Statement
A -> B
Converse Statement
B -> A
Inverse Statement
^{Not}
A ->
^{Not}
B
Contrapositive Statement
^{Not}
B ->
^{Not }
A
Deductive Reasoning
Uses facts to come to a conclusion
Inductive Reasoning
Uses a pattern to determine a conclusion
counter Examples
Prove the statement is false
(ex. All polygons are squares. Prove wrong
: Rectangles etc)
Biconditional statement
If and only if
(ex. If a polygon has three sides than it is a triangle. BICONDITIONAL
: A polygon has three sides if and only if {iff} it is a triangle.
Perpendicular lines Form
A right angle
Law of detatchment
if hypothesis is true, then conclusion is true
Law of Syllagism
EX. Conclude that A -> B
A->N
N->P
P->B
segments are congruent if and only if:
The lengths are equal
If the lines are parallel then:
The corresponding angles are congruent
If two lines are parallel than:
The alternate interior angles are congruent
If two lines are parallel than:
the alternate exterior angles are congruent
If two lines are parallel then:
The consecutive interior angles are supplentary
Slope is
Y = Mx + B
M= slope
B=y intercept
Scalene triangle
all different sides
Isosceles triangle
Two equal sides
Equalatrial triangle
All sides are equal
Equiangular
All angles are equal
Exterior angle theorum:
M<1+M<2= M<3
(measure of angle 1 + measure of angle 2 = measure of angle three)
5 congruence thrms
SAS
: side angle side
SSS
: side side side
HL
: hypotenuse and leg
ASA
: angle side angle
AAS
: angle angle side
if two lines are parallel then their
slopes are the same
Slope formula
Y
_{1}
-Y
_{2 }
/ X
_{1}
-X
_{2}
Point slope formula
Y-Y
_{1}
=M( X-X
_{1 }
)
Translation
slide
reflection
flip
rotation
turn
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
Midsegment of a triangle:
Joins the midpoints.
^{1}
/
_{2 }
length of the longest and parallel to longest side
Concurrent:
Where lines intersect
Point of Concurrency
The point where lines intersect
Circumcenter
Lies on a perpendicular bisector
Perpendicular bisector
perpendicular and bisects a segment
incenter
Lies on the angle bisector
Median of a triangle
Joins vertex and midpoint
Centroid
Lies on medians
Altitude of a triangle
Joins vertex and perpendicular bisector
Ortocenter
lies on the altitude
Relationship between side lengths and angle measures:
longest side opposite largest angle, shortest dise opposite smallest angle
Author
ghstechnology
ID
82463
Card Set
Geometry_semester_1.txt
Description
geometry
Updated
2011-04-28T12:33:44Z
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