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92 Cards in this Set

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Collinear
lies on the same line
Noncollinear
not on the same line
Planes
flat surface that extends indefinitely in all directions. represented by a capitol script letter or 3 pts on teh plane
Line
extends undefinitely in 2 directions
Segment Addition
adding of two parts of a line or two separate lines
Pythagorean Theorem
a^2+b^2=c^2
congruent
=
Segment bisector
a segment, line, or plane that intersects a segment at its midpoint
theorems
a statement that can be proved to appeal to postulates, definations, algebraic properties or rules of logic
Angle
a figure consisting of 2 noncollinear rays with a common endpoint
Ray
starts at a point and continues in one direction forever
Opposite rays
2 rays <a---b---c> such as ba and bc
sides
in an angle the 2 sides that formthe angle, or a segment joining 2 consecutive vertices of the polygon
Vertex
the common endpoint in a ray, the connection of 2 sides
Degrees
unit of measure for angles and arcs
measure
length AB written without the line above it
Right angle
90 degrees
Acute angle
less than 90
Obtuse angle
greater than 90
angle bisector
splits angle into 2 even parts
perpendicular lines
form 90 degree angle
adjacent angle
have a common endpoint and a common side but no common interior sides
Verticle angle
2 non adjacent angles formed by 2 intersecting lines
linear pair
pair of adjacent angles whose noncommon sides are opposite rays
Supplementary
2 angles whos measures add to 180
Complimentary
angle measures add to 90
Inductive Reasoning
Reasoning uses a number of specific examples to arrive at a plausible generalization or prediction. Conclusions arrived at by inductive reasoning lack the logical certainty of those arrived at by deductive reasoning
Counterexample
shows the given statement is not always true
If-then statements
compound statement "if A, then B" where A and B are statements
Conditional Statemetn
A statement in If-then form. If is the hypothesis and then is the conclusion
Hypothesis
in a conditional statement this immediately follows the if
Conclusion
the part following the word then in an if-then statement
Converse
p->q
Negation
denial of a statement
inverse
~p->~q
contrapositive
~q->~p
Deductive reasoning
system of reasoning to reach conclusions which must be true when the assumptions on which the reasoning is based is true
law of detatchment
in a true p->q if p is true then q is true
law of syllogism
if p->q and q->r are true then p->r is also true
parallel lines
lines in the SAME PLANE that dont intersect
skew lines
lines that dont intersect but lie in DIFFERENT planes
transversal
a line that intersects 2 or more lines in a plane at different points
CIA
consecutive interior angles are supplementary if 2 Parallel lines are cut by a transversal
AIA
alternate interior angles congruent
AEA
also congruent
CA
corresponding congruent
Slope
(y2-y1)/(x2-x1)
If and only if
when both conditional and converse are true
Spherical Geometry
branch of geometry that dals with a system of points, great circles (lines), and spheres (planes)
Great Circle
for a given sphere, the intersection of the sphere and a plane taht contains the center of the sphere
Arc
an unbroken part of a circle
Traingle
segments connecting 3 noncollinear points, has 3 parts:interior, exterior, trinagle itself
Polygon
a figure in a plane that meets the conditions: closed and formed by 3 or more coplanar segments, sides that have a common ednpoint are noncollinear, each side intersects exactly 2 other sides but only at endpoints
Acute tringle
a triangle all of whose angles are acute
Obtuse triangle
has one obtuse angle
right triangle
has one right angle
equilateral
3 congruent sides
Scalene
no congruent sides
Isosceles triangle
2 congruent sides and 2 congruent angles ITT
Equiangular Triangle
All angles congruent
Base angles
in an isoceles triangle the angle formed by the base and one of the legs
Triangle sum
180
Auxiliary line
a line or segment added to a given figure to help in proving a result
Congruent Triangles
Traingles with corresponding parts congruent
CPCTC
Congruent parts of congruent triangles are congruent (must prove triangles congruent first)
Included angle
angle formed by 2 sides of a triangle is the inclueded angle for those 2 sides
SSS
3 sides congruent to corrseponding sides on antoher triangle
SAS
side angle side
ASA
angle side angle
AAS
angle angle side
ITT
Isoceles traingel theorem, 2 sides of triangle congruent then the angles opposite the sides are congruent
Perpendicular Bisector
a bisector of a segment that is perpedicular to the segment
median
ina triangle, a segment joins the median of a side and the opposite point
altitude
a segment from the vertex of the triangle to the line containing the opposite side and perpendiular to the line containing that side
Angle Bisector
separates angle into 2 congruent angles
LL
in a right triangle prove conguent by Leg leg
HA
in a right triangle proving congruent by using the hypotenuse and a acute angle of the triangel
LA
in a right triangle uses on leg and an acute angle of the triangle
HL
in a right triangle uses the hypotenuse and the leg
indirect proof
proof by contradiction
EAT
measure of an exterior angle is greater than the sum of the two remote interior angles
quadrilaterals
4 sided polygon
parallelogram def
both pairs of opposite sides parallel
properties of parallelogram
opp. sides congruent, opp. angles congruent, consecutive angles supplementary, diagonals bisect eachother
rectangle def
a quad with four right angles
prop of a rectangle
opp. sides parallel and congruent, opp angles congruent, consec angles supplementary, diagonals bisect and are CONGRUENT
rhombus def
a quad with 4 congruent sides
prop of a rhombus
diagonals are PERPENDICULAR, diagonals bisect opp angles and opp angles are congruent
square
a quad that is a rectangle and rhombus
Trapezoid def
a quad with exactly 1 pair of parallel sides
isoceles trapezoid
has congruent legs
iscoeles trap. prop
diagonals are congruent but dont bisect, midsegment of a trap is the average of base lengths