Geometry Ch. 1 and 2 Word Scramble
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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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