geometry midterm definitions

intuitive ideas, basis of ALL geometry (point, line, and plane)

undefined; a location is space that has no thickness, all figures are made up of points

undefined; extends in opposite directions without ending and has no thickness and cannot be measured. made up of infinite number of points

undefined; a flat surface that goes on forever and has no thickness

the set of ALL points, represented by 4 non-coplanar points

points all in ONE line

points all in ONE plane

the set of all points in both (all) figures

for N to be "between" M and P, all 3 points must be collinear and N must be in the middle

2 points and all points BETWEEN them

segment XY and all points Z, such that Y is between X and Z

collinear rays that share EXACTLY ONE point

statements that are accepted without proof

if B is between A and C, then AB + BC = AC

point that divides a segment into two CONGRUENT segments

objects (or figures) that have the same EXACT size and shape

segments are congruent if and only if their measurements are EQUAL

a line, segment, ray, or plane that intersects a segment at its midpoint

figure formed by two rays that have the endpoint

a point is on the interior of an angle if and only if it lies on a segment whose endpoints are on the angle, but the point is not

angle whose measure is between 0 and 90

angle whose measure is 90

angle whose measure is between 90 and 180

angle whose measure is 180

(NOT WORD FOR WORD) says that every straight line is 180

if point K lines in the interior of angle JGH, the the measure of angle JGK + the measure of angle KGH = the measure of angle JGH

angles that have EQUAL measures

TWO angles IN A PLANE that have a common vertex and a common side but no common interior points

adjacent angles whose non-common sides form opposite rays

the ray that divides and angle into CONGRUENT, adjacent angles

1. 2 points

2. 3 noncollinear points

3. 4 non-coplanar points

there is EXACTLY ONE line

1. one plane

2. plane

then the line that contains the points, is in that plane

then their intersection is a line

then they intersect in EXACTLY ONE point

there is EXACTLY ONE plane

then EXACTLY ONE plane contains the lines

"at least one"; the situation exists, however there could be more than one example

"exactly one"; there is only one example that satisfies a given condition

study of methods and principles that allows you to classify arguments

statements that are either true or false

the joining of 2 or more simple statements

p ^ q; the joining of 2 simple statements with the word "and"

p ⌄ q; joining of 2 simple statements with the word "or"

used to tell under what conditions a compound statement is true or false

TRUE if the first, second, or both statements are true (USED IN OUR CLASS)

implies that the first or second statement are true, but not both

p: Mr. Mann loves football

~p: Mr. Mann does not love football

if p, then q

ex. if you study hard, then you pass the test

expressed as p-> q

you study hard (p)

you pass the test (q)

q -> p

~p -> ~q

~q -> ~p

LAST column of truth table is ALL TRUE

LAST column of truth table is ALL FALSE

to conclude from the given information

the way that affirms by affirming

p -> q

p

therefore, q

p -> q

~q

therefore, ~p

p ^ q

therefore, p

p ⌄ q

~p

therefore, q

p -> q logically equivalent to ~q -> ~p

~(~p) logically equivalent to p

p ^ q LE to q ^ p

p ⌄ q LE to q ⌄ p

(p ^ q) ^ r LE to p ^ (q ^ r)

(p ⌄ q) v r LE to p v (q v r)

p ^ ( q ^ r) LE to (p ^ q) v (p ^ r)

p v (q ^ r) LE to (p v q) ^ (p v r)

~ (p ^ q) LE to ~p v ~q

~ (p v q) LE to ~p ^ ~q

picture that shows logical relationships between sets of data, used to determine whether an argument leads to a valid conclusion

statements are either BOTH true or BOTH false

addition, subtraction, multiplication, division, substitution, reflexive, symmetric, transitive

reflexive, symmetric, transitive

if M is the midpoint of segment AB, then AM = 1/2 AB and MB = 1/2 AB

if ray BX is the bisector of angle ABC, then measure of angle ABX = 1/2 measure of angle ABC and measure of angle XBC = 1/2 measure of ABC

2 angles whose measures have the sum of 90

2 angles whose measures have the sum of 180

2 angles such that the sides of one angle are opposite rays to the sides of the other angle

"vertical angles are congruent"

2 lines that intersect to form at least one RIGHT angle

then they form congruent, adjacent angles

then the lines are perpendicular

then the angles are complementary

then the 2 angles are congruent

then the 2 angles are congruent

coplanar lines that DO NOT intersect

non coplanar lines

planes that DO NOT intersect

they DO NOT intersect

then the lines of intersection are parallel

a line that intersects two or more coplanar lines in different points

2 angles in corresponding positions relative to the 2 lines

2 non-adjacent interior angles on opposite sides of the transversal

2 non-adjacent exterior angles on opposite sides of the transversal

2 interior angles on the same side of the transversal

2 exterior angles on the same side of the transversal

if 2 parallel lines are cut by a transversal, then corresponding angles are congruent

if 2 parallel lines are cut by a transversal, then alternate interior angles are congruent

if 2 parallel lines are cut by a transversal, then same side interior angles are supplementary

if 2 parallel lines are cut by a transversal, then alternate exterior angles are congruent