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92 Cards in this Set
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 Back
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 <abc> 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


Ifthen statements

compound statement "if A, then B" where A and B are statements


Conditional Statemetn

A statement in Ifthen 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 ifthen 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

(y2y1)/(x2x1)


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
