Geometry
Card Set Information
Author:
ECCammi
ID:
192843
Filename:
Geometry
Updated:
2013-01-14 19:44:29
Tags:
Math Notes final
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Description:
Final geometry math notes
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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
Non-coplanar, 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
point slope form
Conjectures
Logical conclusions based on reasoning
Counterexamples
One example to show a conjecture is false
Conditional statements
if-then statements
p-> q
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 a-c=b-c
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 3-10
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
Polygon
A closed plane
Total degrees in a polygon
(n-2)180
Slope intercept form
y=mx+b
standard form
ax+by=c
point slope form
y-y
_{1}
=m(x
_{1}
-x
_{2}
)
SAS side-angle-side
Same side, angle and another side
SSS Side side side
three side are all congruent
AAA
Doesn't work
ASA
Equal angle, side and another angle
SAA/AAS
Side Angle Angle
H-L 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 5-2
If a point is the perp. bisector of a segment then it is equidistant from the endpoints of the segment
Theorem 5-3
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 5-4
If a point is on the bisector of an angle then it is equidistant to each side of angles
Theorem 5-5
Th. 5-4 converse