# Untitled

## 66 terms · Stuff you need to know to pass Matt's test

### deductive reasoning

uses logic to draw conclusion from statements already acccepted as true

### inductive reasoning

drawing conclusions through a limited set of observations

### point

refers to a location on a plane

### line

straight, endless arrangement of points going on in both directions

### line segment

part of a line bounded by 2 endpoints...can be measured

space

on the same line

### non collinear

can never be on the same line

### ray

a line that extends from a point and goes on forever in one direction

### angle

a pair of rays with the same endpoint

### polygon

a connected set of at least 3 line segments in the same plane such that each segment intersects exactly 2 others

### polyhedron

bounded by polygons, exist in space, and is 3 dimensional

### perimeter

sum of all the sides

### area

number of units squares equal in measure to it's surface

### coplanar

points on the same plane

### concurrent

lines that contain the same point

### commutative

(A+B = B+A) you can switch adding order

### associative

(a+b)+c=a+(b+c) you can move brackets around

### identity

a+0=a do something to make it itself

### inverse

a+(-a)=0 the what you started with the opposite

### conditional statement

P-->Q statements..if rain, then wet.

P or the if part

### conclusion

Q or the then part

### converse

reversing the conditional statement

### theorem

a statement that is proved by reasoning deductively

### indirect proof

assume the opposite then prove by contradiction

### postulate

assumed to be true without proof

### postulate one

2 point determine a line

### postulate 2

3 noncollinear points determine a plane

### deductive system

a logical system of constructing proofs using definitions, postulates and theorems

if and only if

### triangle angle sum

sum of all angles equals 180

### reflexive property

a=a...any # is equal to itself

### substitution property

if a = b, then a can be used for b in any expression

### addition property

if a=b, then a+c = b+c

### subtraction property

if a=b, then a-c = b-c

### multiplication property

if a=b, then ac = bc

### division property

if a = b and c is not zero, then a/c = b/c

### ruler postulate

i can use my ruler to measure stuff

### betweeness of points

A-B-C iff a<b<c or a>b>c

### betweeness of points theorem

if A-B-C, then AB+BC = AC

### obtuse

iff more than 90 but less than 180

### betweeness of rays theorem

if OA-OB-OC, then AOB+BOC = AOC

### corollary

can be easily proved from a postulate or another theorem

### vertical angle theorem

vertical angles are equal

### parallel

lie on the same plane but never intersect

### congruent

if a shape is congruent there is a correspondence between their vertics and all sides are equal and correspond

### corollary to congruent

2 triangles congruent to a 3rd triangle are congruent to eachother

### ASA postulate

if 2 angles and the included side of one triangle are equal to two angles and the included side of another triandle, the triangles are congruent

### SAS postulate

if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent

### theorem 9

if 2 sides of a triangle are equal the angles opposite them are equal

### theorem 10

if 2 angles of a triangle are equal the sides opposite them are equal

### SSS theorem

if three sides of one triangle are equal to the three sides of another, the triangles are congruent

### 3 possibilities property

either a>b, a<b, or a=b

### transitive property

if a>b and b>c, then a>c

### addition property

if a>b, then a+c > b+c

### subtraction property

if a>b, then a-c> b-c

### multiplication property

if a>b and c>0, then ac > bc

### division property

if a>b and c>o, then a/c >b/c

### addition theorem of inequality

if a>b and c>d, then a+c > b+d

### whole greater than part theorem

if a>0, b>0, and a+b=c, then c>a and c>b

### exterior angle

a angle that forms a linear pair with an angle of the trianle

### exterior angle theorem

an exterior angle of a triangle is greater than either remote interior angle

### theorem 13

if 2 sides of a triangles are unequal then angles opposite them are unequal in the same order

### theorem 14

if 2 anles of a triangle are unequal, the sides opposite them are unequal in the same order

### triangle inequality theorem

the sum of any 2 sides of a triangle is greater than the third side