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# Geometry Ch. 1 and 2

Question | Answer |
---|---|

point | a location. it has neither shape nor size. |

line | made up of points and has no thickness or width. exactly one through any two points. |

plane | a flat surface made up of points that extends infinitely in all directions. there is exactly one through any three points not on the same line. |

collinear | points that lie on the same line. |

coplanar | points that lie on the same plane. |

intersection | two or more geometric figures is the set of points they have in common. two lines = point 2 planes = line |

space | defined as boundless, three dimensional set of all points |

line segment | can be measured because it has two endpoints |

Betweenness of points | for any two points A and B on a line, there is another point C between A and B if and only if A, B, and C are collinear and AC+CB=AB |

Congruent Segments | segments that have the same measure |

Constructions | are methods of creating these figures without the benefit of measuring tools |

distance | between two points is the length of the segment with those points as its endpoints √(x2-x1)² + (y2-y1)² |

midpoint | is the point halfway between the endpoints of the segment m= (x1 + x2)/2 |

segment bisector | any segment, line, or plane that intersects a segment at its midpoint |

ray | a part of a line. it has one endpoint and extends indefinitely in one direction |

opposite rays | if you choose a point on a line, the point determines exactly two rays called this. since both rays share a common enpoint, ______ are collinear |

angle | formed by two noncollinear rays that have a common endpoint. |

sides | the rays are called this of the angle |

vertex | the common endpoint |

interior | inside of angle |

exterior | outside of angle |

degrees | angles are measured in units |

right angle | measure = 90 |

acute angle | measure = less than 90 |

obtuse angle | measure = more than 90 |

angle bisector | a ray that divides an angle into two congruent angles |

adjacent angles | two angles that lie in the same plane and have a common vertex and a common side but no common interior points |

linear pair | a pair of adjacent angles with noncommon sides that are opposite rays |

vertical angles | two nonadjacent angles formed by two intersecting lines |

complementary angles | two angles with measures that have a sum of 90 |

supplementary angles | are two angles with measures that have a sum of 180 |

perpendicular | lines, segments, or rays that form right angles |

polygon | a closed figure by a finite number of coplanar segments called sides |

vertex of the polygon | vertex of each angle |

concave | some of the lines pass through the interior |

convex | no points of the lines are in the interior |

n~gon | a polygon with n sides |

regular polygon | a convex polygon that is both equilateral and equiangular |

equilateral polygon | a polygon in which all sides are congruent |

equiangular polygon | a polygon in which all angles are congruent |

perimeter | the sum of the lengths of the sides of the polygon |

circumference | of circle is the distance around the circle |

area | the number of square units needed to cover a surface |

polyhedron | a solid with all flat surfaces that enclose a single region of space |

face | each flat surface of a polygon |

edges | the line segments where the faces intersect |

vertex | the point where three or more edges intersect |

prism | a polyhedron with two parallel congruent faces called bases connected by parallelogram faces |

base of a polyhedron | the two parallel congruent faces of a polyhedron |

pyramid | a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex |

cylinder | a solid with congruent parallel circular bases connected by curved surfaces |

cone | a solid with a circular base connected by a curved surface to a single vertex |

regular polyhedron | if all of its faces are regular congruent polygons and all of the edges are congruent |

platonic solids | exactly five types of regular polyhedrons |

surface area | two- dimensional measurement of the surface of a solid figure |

volume | the measure of the amount of space enclosed by a solid figure |

inductive reasoning | reasoning that uses a number of specific examples to arrive at a conclusion |

conjecture | a concluding statement reached using inductive reasoning |

counterexample | false example, called this, and it can be a number, drawing, or statement. |

statement | a sentence that is either true or false |

truth value | a statement is either t or f represented using p and q |

negation | has the opposite meaning as well as an opposite truth value. not p or ~p |

conjunction | a compound statement using the word and |

truth table | a convenient method for organizing truth values of statements |

disjunction | a compound statement using the word or |

pyramid | a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex |

cylinder | a solid with congruent parallel circular bases connected by curved surfaces |

cone | a solid with a circular base connected by a curved surface to a single vertex |

sphere | a set of point in the space that are the same distance from a given point. no faces, edges, or vertices |

regular polyhedron | if all of its faces are regular congruent polygons and all of the edges are congruent |

platonic solids | exactly five types of regular polyhedrons |

surface area | two- dimensional measurement of the surface of a solid figure |

volume | the measure of the amount of space enclosed by a solid figure |

inductive reasoning | reasoning that uses a number of specific examples to arrive at a conclusion |

conjecture | a concluding statement reached using inductive reasoning |

counterexample | false example, called this, and it can be a number, drawing, or statement. |

statement | a sentence that is either true or false |

truth value | a statement is either t or f represented using p and q |

negation | has the opposite meaning as well as an opposite truth value. not p or ~p |

compound statement | the statement formed from two or more simple statements using connective words like "and" or "or." |

conjunction | a compound statement using the word "and" |

disjunction | a compound statement using the word "or" |

truth table | a convenient method for organizing truth values of statements |

if-then statements | if p, then q |

hypothesis | conditional statement is the phrase immediately following the word if... p |

conclusion | conditional statement is the phrase immediately following the word then... q |

related conditionals | there are other statements that are based on a given conditional |

converse | exchanging the hypothesis and conclusion of the conditional..... q-p |

inverse | formed by negating both the hypothesis and conclusion of the conditional...... ~p - ~q |

contrapositive | formed by negating both the hypothesis and the conclusion of the converse of the conditional..... ~q - ~p |

logically equivalent | statements with the same truth values |

deductive reasoning | uses facts, rules, definitions, or properties to reach logical conclusions from given statements |

valid | method of proving a conjecture |

law of detachment | one valid form of deductive reasoning if p - q is a true statement and p is true then q is true |

postulate or axiom | is a statement that is accepted as true without proof |

postulate 2.1 | through any two points, there is exactly one line |

postulate 2.2 | through any three noncollinear points, there is exactly one plane |

postulate 2.3 | a line contains at least two points |

postulate 2.4 | a plane contains at least three noncollinear points |

postulate 2.5 | if two points lie in a plane, then the entire line containing those points lies in that plane |

postulate 2.6 | if two line intersect, then their intersection is exactly one point |

postulate 2.7 | if two planes intersect then their intersection is a line |

proof | a logical argument in which each statement you make is supported by a statement this is accepted as true |

deductive argument | a proof formed by a group of algebraic steps used to solve a problem |

paragraph proof | an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true |

informal proofs | a paragraph proof |

midpoint theorem | if M is the midpoint of segment AB, then seg. AM is congruent to seg. MB. A_______M_______B |

addition property of equality | if a = b then a + c = b + c |

subtraction property of equality | if a = c then a - c = b - c |

multiplication prop of equality | if a = b then a*c=b*c |

division prop of equality | if a = b and c ≠ 0 then a /c = b/c |

reflexive prop of equality | a = a |

symmetric prop of equality | if a = b then b = a |

transitive prop of equality | if a = b and b = c then a = c |

substitution prop of equality | if a = c then a may b replaced by b in any equation of expression |

distributive prop | a(b + c) = ab + ac |

algebraic proof | is a proof that is made up of a series of algebraic statement |

two-column proof or formal proof | contains statements and reasons organized in two columns |

ruler postulate | the points on any line or line segment can be put into one-to-one correspondence with real numbers |

segment addition postulate | if A, B, and C are collinear, the point B is between A and C if and only if AB+BC=AC |

Reflexive prop of congruence | seg. AB ≅ seg. AB |

symmetric prop of congruence | if seg. AB ≅ seg. CD, the seg. CD ≅ seg. AB |

Transitive prop of congruence | if seg. AB ≅ seg. CD and seg. CD ≅ seg. EF then seg. AB ≅ seg. EF |

Protractor Postulate | given any angle, the measure can be put into one- to- one correspondence with real numbers between 0 and 180 |

angle addition postulate | states that if D is in the interior of angle ABC, then the measure of angle ABD + the measure of angle DBC = the measure of angle ABC. |

Supplement Theorem | if two angles form a linear pair, then they are supplementary angles |

Complement Theorem | if the noncommon sides of two adjacent angles form a right angle then the angles are complentary angles |

Reflexive prop of congruence | ∠1 ≅ ∠1 |

Symmetric prop of congruence | if ∠1 ≅ ∠2 then ∠2 ≅ ∠1 |

transitive prop of congruence | if ∠1 ≅ ∠2 and ∠2 ≅ ∠3 then ∠1 ≅ ∠3 |

Congruent Supplements Theorem | Angles supplementary to the same angle or to congruent angles are congruent |

Vertical Angles Theorem | if two angles are vertical angles then they are congruent |

Right angle theorem 2.9 | perpendicular lines intersect to form four right angles |

Right angle theorem 2.10 | all right angles are congruent |

Right Angle theorem 2.11 | perpendicular lines form congruent adjacent angles |

Right Angle theorem 2.12 | if two angles are congruent and supplementary then each angle is a right angle |

Right Angle theorem 2.13 | if two congruent angles form a linear pair, then they are right angles |