Geometry_semester_1.txt
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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
YY_{1}=M( XX_{1 })




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


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