Geometry
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Collinear Points
2 points that make up a line

Plane
Flat surface with no thickness

Line segment
Segment of a line with an end point

Opposite rays
Form a line while sharing a point

Skew lines
Noncoplanar, never intersecting lines

Congruent segments
2 segments with the same length

Perpendicular bisector
Line, segment or ray that is perpendicular to the segment at the midpoint

Angle bisector
A ray that divides an angle into two congruent coplanar angles

Complementary angles
Add to 90^{0}

Supplementary angles
Add to 180^{0}

Adjacent angles
2 angles next to each other that share a side

Vertical angles
 formed by 2 lines intersecting
 They are congruent




Conjectures
Logical conclusions based on reasoning

Counterexamples
One example to show a conjecture is false


Hypothesis
 The part that follows the if
 p

Conclusion
 Part that follows the "then"
 q

Converse
 Reverse of the conditional
 q>p

Biconditional
 conditional and converse are true
 p<>q

Deductive reasoning
Process of reasoning logically from given statements to reach a conclusion

Detachment
 If the conditional is T; + hypothesis is T then conclusion is T
 p>q is T, p> T, then q>T

Syllogism
2 conditionals if conclusion of one being the hypothesis of next

Addtional equality property
if a=b then a+c=b+c

Equality property of Subtraction
if a=b then ac=bc

Equality property of Multiplication
if a=b then ac=bc

Equality property of divsion
if a=b then a/c=b/c

Reflexive equality property
a=a

Symmetric property of equality
if a=b then b=a

Transitive property of equality
a=b then b can replace a anywhere

Distributive property of equality
if a(b+c) =ab+ac

SSI Same side interior angles (between parallels)
Are congruent angles

Transversal line
Crosses both lines

AIA alternate interior angles
Are congruent

Therom 310
if 2 lines are perpendicular to the same line then they are parallel to each other

Equilateral triangle
Three sides are equal

Isosceles
Two sides are equal length

Scalene
All sides are different length


Total degrees in a polygon
(n2)180

Slope intercept form
y=mx+b


point slope form
yy_{1}=m(x_{1}x_{2})

SAS sideangleside
Same side, angle and another side

SSS Side side side
three side are all congruent


ASA
Equal angle, side and another angle


HL therom
 1. 2 right angles
 2. Triangles have congruent hypotenuses
 3. A pair of congruent legs
 SSA works here

Hypotenuse
Side opposite of the right anle/vertex

CPCTC
Corresponding pars of congruent triangles are congruent

Triangle midsegment theorem
midsegment parallel = 2(midsegment)

Theorem 52
If a point is the perp. bisector of a segment then it is equidistant from the endpoints of the segment

Theorem 53
If a point is equidistant from both endpoints then it must be on the perp. bisector

Locus
Set of all points that meet a condition

Theorem 54
If a point is on the bisector of an angle then it is equidistant to each side of angles

Theorem 55
Th. 54 converse