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Collinear
Points on the same line
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Coplaner
points on the same plane
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Non collinear
points not on the same line
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non coplaner
points not on the same plane
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area of a Rectangle
Base x height
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area of a triangle
Base x height / 2
b x h / 2
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Area of a parallelagram
Base x Height
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Area of a circle
A= Pi(r2)
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Circumference of a circle
C= Pi (d)
D= diameter
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diameter of a circle
D=2r
r=Radius
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Complementary angle is equal to :
90 degrees
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Supplementary angle is equal to :
180 degrees
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Midpoint formula
M = (X1 + X2 / 2 , Y1+ Y2 / 2)
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Endpoint formula
( X1+ X / 2 = X2 , Y1+ Y / 2 = Y2 )
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Distance Formula
D = [ ( x1-x2 )2 + ( y1-y2 )2
[ = square root sign
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Linear pair
Two angles that create a line
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Theorem: All verticle angles are....
Congruent
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Acute angle
Less than 90 degrees
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Obtuse angle
More than 90 degrees
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Straight angle
180 degrees
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To bisect an angle is to
cut it in half
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Adjacent angles are
next to eachother. no overlapping
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Conditional Statement
A -> B
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Converse Statement
B -> A
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Inverse Statement
Not A -> Not B
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Contrapositive Statement
Not B -> Not A
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Deductive Reasoning
Uses facts to come to a conclusion
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Inductive Reasoning
Uses a pattern to determine a conclusion
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counter Examples
- Prove the statement is false
- (ex. All polygons are squares. Prove wrong: Rectangles etc)
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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.
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Perpendicular lines Form
A right angle
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Law of detatchment
if hypothesis is true, then conclusion is true
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Law of Syllagism
- EX. Conclude that A -> B
- A->N
- N->P
- P->B
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segments are congruent if and only if:
The lengths are equal
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If the lines are parallel then:
The corresponding angles are congruent
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If two lines are parallel than:
The alternate interior angles are congruent
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If two lines are parallel than:
the alternate exterior angles are congruent
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If two lines are parallel then:
The consecutive interior angles are supplentary
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Slope is
- Y = Mx + B
- M= slope
- B=y intercept
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Scalene triangle
all different sides
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Isosceles triangle
Two equal sides
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Equalatrial triangle
All sides are equal
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Equiangular
All angles are equal
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Exterior angle theorum:
- M<1+M<2= M<3
- (measure of angle 1 + measure of angle 2 = measure of angle three)
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5 congruence thrms
- SAS: side angle side
- SSS: side side side
- HL: hypotenuse and leg
- ASA: angle side angle
- AAS: angle angle side
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if two lines are parallel then their
slopes are the same
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Slope formula
Y1-Y2 / X1-X2
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Point slope formula
Y-Y1=M( X-X1 )
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CPCTC
Corresponding Parts of Congruent Triangles are Congruent
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Midsegment of a triangle:
Joins the midpoints. 1/2 length of the longest and parallel to longest side
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Concurrent:
Where lines intersect
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Point of Concurrency
The point where lines intersect
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Circumcenter
Lies on a perpendicular bisector
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Perpendicular bisector
perpendicular and bisects a segment
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incenter
Lies on the angle bisector
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Median of a triangle
Joins vertex and midpoint
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Altitude of a triangle
Joins vertex and perpendicular bisector
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Ortocenter
lies on the altitude
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Relationship between side lengths and angle measures:
longest side opposite largest angle, shortest dise opposite smallest angle
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