Geometry Ch. 1 and 2
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| point | a location. it has neither shape nor size.
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| line | made up of points and has no thickness or width. exactly one through any two points.
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| 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.
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| collinear | points that lie on the same line.
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| coplanar | points that lie on the same plane.
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| intersection | two or more geometric figures is the set of points they have in common. two lines = point 2 planes = line
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| space | defined as boundless, three dimensional set of all points
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| line segment | can be measured because it has two endpoints
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| 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
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| Congruent Segments | segments that have the same measure
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| Constructions | are methods of creating these figures without the benefit of measuring tools
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| distance | between two points is the length of the segment with those points as its endpoints
√(x2-x1)² + (y2-y1)²
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| midpoint | is the point halfway between the endpoints of the segment m= (x1 + x2)/2
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| segment bisector | any segment, line, or plane that intersects a segment at its midpoint
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| ray | a part of a line. it has one endpoint and extends indefinitely in one direction
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| 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
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| angle | formed by two noncollinear rays that have a common endpoint.
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| sides | the rays are called this of the angle
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| vertex | the common endpoint
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| interior | inside of angle
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| exterior | outside of angle
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| degrees | angles are measured in units
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| right angle | measure = 90
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| acute angle | measure = less than 90
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| obtuse angle | measure = more than 90
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| angle bisector | a ray that divides an angle into two congruent angles
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| adjacent angles | two angles that lie in the same plane and have a common vertex and a common side but no common interior points
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| linear pair | a pair of adjacent angles with noncommon sides that are opposite rays
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| vertical angles | two nonadjacent angles formed by two intersecting lines
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| complementary angles | two angles with measures that have a sum of 90
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| supplementary angles | are two angles with measures that have a sum of 180
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| perpendicular | lines, segments, or rays that form right angles
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| polygon | a closed figure by a finite number of coplanar segments called sides
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| vertex of the polygon | vertex of each angle
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| concave | some of the lines pass through the interior
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| convex | no points of the lines are in the interior
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| n~gon | a polygon with n sides
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| regular polygon | a convex polygon that is both equilateral and equiangular
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| equilateral polygon | a polygon in which all sides are congruent
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| equiangular polygon | a polygon in which all angles are congruent
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| perimeter | the sum of the lengths of the sides of the polygon
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| circumference | of circle is the distance around the circle
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| area | the number of square units needed to cover a surface
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| polyhedron | a solid with all flat surfaces that enclose a single region of space
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| face | each flat surface of a polygon
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| edges | the line segments where the faces intersect
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| vertex | the point where three or more edges intersect
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| prism | a polyhedron with two parallel congruent faces called bases connected by parallelogram faces
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| base of a polyhedron | the two parallel congruent faces of a polyhedron
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| pyramid | a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex
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| cylinder | a solid with congruent parallel circular bases connected by curved surfaces
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| cone | a solid with a circular base connected by a curved surface to a single vertex
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| regular polyhedron | if all of its faces are regular congruent polygons and all of the edges are congruent
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| platonic solids | exactly five types of regular polyhedrons
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| surface area | two- dimensional measurement of the surface of a solid figure
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| volume | the measure of the amount of space enclosed by a solid figure
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| inductive reasoning | reasoning that uses a number of specific examples to arrive at a conclusion
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| conjecture | a concluding statement reached using inductive reasoning
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| counterexample | false example, called this, and it can be a number, drawing, or statement.
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| statement | a sentence that is either true or false
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| truth value | a statement is either t or f represented using p and q
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| negation | has the opposite meaning as well as an opposite truth value. not p or ~p
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| conjunction | a compound statement using the word and
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| truth table | a convenient method for organizing truth values of statements
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| disjunction | a compound statement using the word or
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| pyramid | a polyhedron that has a polygonal base and three or more triangular faces that meet at a common vertex
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| cylinder | a solid with congruent parallel circular bases connected by curved surfaces
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| cone | a solid with a circular base connected by a curved surface to a single vertex
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| sphere | a set of point in the space that are the same distance from a given point. no faces, edges, or vertices
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| regular polyhedron | if all of its faces are regular congruent polygons and all of the edges are congruent
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| platonic solids | exactly five types of regular polyhedrons
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| surface area | two- dimensional measurement of the surface of a solid figure
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| volume | the measure of the amount of space enclosed by a solid figure
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| inductive reasoning | reasoning that uses a number of specific examples to arrive at a conclusion
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| conjecture | a concluding statement reached using inductive reasoning
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| counterexample | false example, called this, and it can be a number, drawing, or statement.
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| statement | a sentence that is either true or false
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| truth value | a statement is either t or f represented using p and q
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| negation | has the opposite meaning as well as an opposite truth value. not p or ~p
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| compound statement | the statement formed from two or more simple statements using connective words like "and" or "or."
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| conjunction | a compound statement using the word "and"
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| disjunction | a compound statement using the word "or"
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| truth table | a convenient method for organizing truth values of statements
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| if-then statements | if p, then q
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| hypothesis | conditional statement is the phrase immediately following the word if... p
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| conclusion | conditional statement is the phrase immediately following the word then... q
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| related conditionals | there are other statements that are based on a given conditional
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| converse | exchanging the hypothesis and conclusion of the conditional..... q-p
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| inverse | formed by negating both the hypothesis and conclusion of the conditional...... ~p - ~q
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| contrapositive | formed by negating both the hypothesis and the conclusion of the converse of the conditional..... ~q - ~p
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| logically equivalent | statements with the same truth values
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| deductive reasoning | uses facts, rules, definitions, or properties to reach logical conclusions from given statements
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| valid | method of proving a conjecture
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| law of detachment | one valid form of deductive reasoning
if p - q is a true statement and p is true then q is true
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| postulate or axiom | is a statement that is accepted as true without proof
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| postulate 2.1 | through any two points, there is exactly one line
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| postulate 2.2 | through any three noncollinear points, there is exactly one plane
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| postulate 2.3 | a line contains at least two points
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| postulate 2.4 | a plane contains at least three noncollinear points
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| postulate 2.5 | if two points lie in a plane, then the entire line containing those points lies in that plane
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| postulate 2.6 | if two line intersect, then their intersection is exactly one point
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| postulate 2.7 | if two planes intersect then their intersection is a line
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| proof | a logical argument in which each statement you make is supported by a statement this is accepted as true
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| deductive argument | a proof formed by a group of algebraic steps used to solve a problem
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| paragraph proof | an informal proof written in the form of a paragraph that explains why a conjecture for a given situation is true
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| informal proofs | a paragraph proof
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| midpoint theorem | if M is the midpoint of segment AB, then seg. AM is congruent to seg. MB. A_______M_______B
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| addition property of equality | if a = b then a + c = b + c
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| subtraction property of equality | if a = c then a - c = b - c
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| multiplication prop of equality | if a = b then a*c=b*c
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| division prop of equality | if a = b and c ≠ 0 then a /c = b/c
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| reflexive prop of equality | a = a
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| symmetric prop of equality | if a = b then b = a
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| transitive prop of equality | if a = b and b = c then a = c
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| substitution prop of equality | if a = c then a may b replaced by b in any equation of expression
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| distributive prop | a(b + c) = ab + ac
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| algebraic proof | is a proof that is made up of a series of algebraic statement
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| two-column proof or formal proof | contains statements and reasons organized in two columns
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| ruler postulate | the points on any line or line segment can be put into one-to-one correspondence with real numbers
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| 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
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| Reflexive prop of congruence | seg. AB ≅ seg. AB
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| symmetric prop of congruence | if seg. AB ≅ seg. CD, the seg. CD ≅ seg. AB
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| Transitive prop of congruence | if seg. AB ≅ seg. CD and seg. CD ≅ seg. EF then seg. AB ≅ seg. EF
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| Protractor Postulate | given any angle, the measure can be put into one- to- one correspondence with real numbers between 0 and 180
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| 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.
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| Supplement Theorem | if two angles form a linear pair, then they are supplementary angles
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| Complement Theorem | if the noncommon sides of two adjacent angles form a right angle then the angles are complentary angles
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| Reflexive prop of congruence | ∠1 ≅ ∠1
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| Symmetric prop of congruence | if ∠1 ≅ ∠2 then ∠2 ≅ ∠1
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| transitive prop of congruence | if ∠1 ≅ ∠2 and ∠2 ≅ ∠3 then ∠1 ≅ ∠3
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| Congruent Supplements Theorem | Angles supplementary to the same angle or to congruent angles are congruent
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| Vertical Angles Theorem | if two angles are vertical angles then they are congruent
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| Right angle theorem 2.9 | perpendicular lines intersect to form four right angles
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| Right angle theorem 2.10 | all right angles are congruent
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| Right Angle theorem 2.11 | perpendicular lines form congruent adjacent angles
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| Right Angle theorem 2.12 | if two angles are congruent and supplementary then each angle is a right angle
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| Right Angle theorem 2.13 | if two congruent angles form a linear pair, then they are right angles
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You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
15jsmith
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