Math Vocab Issue 13

• Math  3/21
• Vocabulary
• CHAPTER 1:
• A collinear set of points is a set of points all of which lie on the same straight line
• A noncollinear set of points is a set of three or more points that do not all lie on the same straight line
• The distance between two points on the real number line is the absolute value of the difference of the coordinates of the two points
• B is between A and C if and only if A, B, and C are distinct collinear points and AB + BC = AC
• A line segment, or a segment, is a set of points consisting of two points on a line, called endpoints, and all of the points on the line between the endpoints
• The length or measure of a line segment is the distance between its endpoints
• Congruent segments are segments that have the same measure
• The midpoint of a line segment is a point of that line segment that divides the segment into two congruent segments
• The bisector of a line segment is any line, or subset of a line, that intersects the segment at its midpoint
• A line segment, RS, is the sum of two line segments, RP and PS, if P is between R and S
• Two points, A and B, are on one side of a point P if A, B, and P are collinear and P is not between A and B
• A half-line is a set of points on one side of a point
• A ray is a part of a line that consists of a point on the line, called an endpoint, and all the points on one side of the endpoint
• Opposite rays are two rays of the same line with a common endpoint an no other point in common
• An angle is a set of points that is the union of two rays having the same endpoint
• A straight angle is an angle that is the union of opposite rays and whose degree measure is 180
• An acute angle is an angle whose degree measure is greater than 0 and less than 90
• A right angle is an angle whose degree measure is 90
• An obtuse angle is an angle whose degree measure is grater than 90 and less than 180
• Congruent angles are angles that have the same measure
• A bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides that angle into two congruent angles
• Perpendicular lines are two lines that intersect to form right angles
• The distance from a point to a line is the length os the perpendicular from the point to the line
• If point P is a point on the interior of Angle RST and Angle RST is not a straight angle, or if P is any point not on straight angle RST, then Angle RST is the sum of two angles, Angle RSP and Angle PST
• A polygon is a closed figure in a plane that is the union of line segments such that the segments intersect only at their endpoints and no segments sharing a common endpoint are collinear
• A triangle is a polygon that has exactly three sides
• A scalene triangle is a triangle with no congruent sides
• An isosceles triangle is a triangle that has two congruent sides
• An equilateral triangle is a triangle that has three congruent sides
• An acute triangle is a triangle that has three acute angles
• A right triangle is a triangle that has a right angle
• An obtuse triangle is a triangle that has an obtuse angle
• An equiangular triangle is a triangle that has three congruent angles
• CHAPTER 2:
• Logic is the study of reasoning
• In logic, a mathematical sentence is a sentence that contains a complete thought and can be judged to be true or false
• A phrase is an expression that is only part of a sentence
• An open sentence is any sentence that contains a variable
• The domain or replacement set is the set of numbers that can replace a variable
• The solution set or truth set is the set of all replacements that will change an open sentence to true sentences
• A statement or a closed sentence is a sentence that can be judged to be true or false
• A closed sentence is said to have a truth value, either true (T) or false (F)
• The negation of a statement has the opposite truth value of a given statement
• In logic, a compound sentence is a combination of two or more mathematical sentences formed by using the connectives not, and, or, if...then, or if and only if
• A conjunction is a compound statement formed by combining two simple statements, called conjuncts, with the word and. The conjunction P and Q is written symbolically as P ^ Q
• A disjunction is a compound statement formed by combining two simple statements, called disjuncts, with or. The disjunction P or Q is written symbolically as P \/ Q
• A truth table is a summary of all possible truth values of a logic statement
• A conditional compound statement formed by using the words if...then to combine two simple statements. The conditional if P then Q is written symbolically as P -> Q
• A hypothesis, also called a premise or antecedent, is an assertion that begins an argument. The hypothesis usually follows the word if
• A conclusion, also called a consequent, is an ending or a sentence that closes an argument. The conclusion usually follows the word then
• The inverse of a conditional is formed by negating the hypothesis and conclusion
• The converse of a conditional is formed by interchanging the hypothesis and the conclusion
• The contrapositive of a conditional if formed by interchanging and negating, both the hypothesis and conclusion
• Two statements are logically equivalent or logical equivalents if they always have the same truth value
• A biconditional is a compound statement formed by the conjunction ( P->Q) and its converse (Q->P)
• A valid argument uses a series of statements called premises that have known truth values to arrive at a conclusion
• CHAPTER 3:
• Postulates - 3.1 The Reflexive property of equality: a=a
• 3.2 The Symmetric Property of Equality: if a=b, then b=a
• 3.3 The Transitive Property of Equality: if a=b and b=c, then a=c
• 3.4 A quantity may be substituted for its equal in any statement of equality
• 3.5 A whole is equal to the sum of all its parts
• 3.5.1 A segment is congruent to the sum of all its parts
• 3.5.2 A angle is congruent to the sum of all its parts
• 3.6 If equal quantities are added to equal quantities, the sums re equal
• 3.6.1 If congruent segments are added to congruent segments, the sums are congruent
• 3.6.2 If congruent angles are added to congruent angles, the sums are congruent
• 3.7 If equal quantities are subtracted from equal quantities, the differences are equal
• 3.7.1 If congruent segments are subtracted from congruent segments, the differences are congruent
• 3.7.2 If congruent angles are subtracted from congruent angles, the differences are congruent
• 3.8 If equals are multiplied by equals, the products are equal
• 3.9 Doubles of equal quantities are equal
• 3.10 If equals are divided by nonzero equals, the quotients are equal
• 3.11 Halves of equal quantities are equal
• 3.12 The squares of equal quantities are equal
• 3.13 The positive square roots of equal quantities are equal
• CHAPTER 4:
• Adjacent angles are two angles in the same plane that have a common vertex and a common side but do not have any interior points in common
• Complementary angles are two angles the sum of whose degree measures is 90
• Supplementary angles are two angles the sum of whose degree measures 180
• A linear pair of angles are two adjacent whose sum is a straight angle
• Vertical angles are two angles in which the sides of one angle are opposite rays to the sides of the second angle
• Two polygons are congruent if and only if there is one-to-one correspondence between their vertices such that corresponding angles are congruent and corresponding sides are congruent
• -Corresponding parts of congruent polygons are congruent
• -Corresponding parts of congruent polygons are equal in measure
• Postulates - 4.1 A line segment can be extended to any length in either direction
• 4.2 Through two given points, one and only one line can be drawn (two points determine a line)
• 4.3 Two lines cannot intersect in more than one point 
• 4.4 One and only one circle can be drawn with any given point as center and 
• 4.5 At a given point on a given line, one and only one perpendicular can be drawn to the line
• 4.6 From a given point not on a given line, one and only one perpendicular can be drawn to the line
• 4.7 For any two distinct points, there is only one positive real number that is the length of the line segment joining the two points (Distance Postulate)
• 4.8 The shortest distance between two points is the length of the line segment joining these two points
• 4.9 A line segment has one and only one midpoint
• 4.10 An angle has one and only one bisector
• 4.11 Any geometric figure is congruent to itself ( Reflexive Property )
• 4.12 A congruence can be expressed in either order ( Symmetric Property )
• 4.13 Two geometric figures congruent to the same geometric figure are congruent to each other ( Transitive Property )
• 4.14 Two triangles are congruent if two sides and the included angle of one triangle are congruent, respectively, to two sides and the included angle of the other ( SAS )
• 4.15 Two triangles are congruent if two angles and the included side of one triangle are congruent, respectively, to two angles and the included side of the other ( ASA )
• 4.16 Two triangles are congruent if the three sides of one triangle are congruent, respectively, to the three sides of the other
• Theorems - 4.1 If two angles are right angles, then they are congruent
• 4.2 If two angles are straight angles, then they are congruent
• 4.3 If two angles are complements of the same angle, then they are congruent
• 4.4 If two angles are congruent, then their complements are congruent
• 4.5 If two angles are supplements of the same angle, then they are congruent
• 4.6 If two angles are congruent, then their supplements are congruent
• 4.7 If two angles form a linear pair, then they are supplementary
• 4.8 If two lines intersect to from congruent adjacent angles, then they are perpendicular
• 4.9 If tow lines intersect, then the vertical angles are congruent
• ‎(c) VLAD 2012
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