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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 |
Created by:
15jsmith
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