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26 Cards in this Set
- Front
- Back
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HYPOTHESIS |
A hypothesis is the "if" part (antecedent) of a conditional statement. |
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CONCLUSION |
A conclusion is the "then" part of a conditional statement. |
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BY CONDITIONAL |
A conditional statement, symbolized by pq, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . The conditional is defined to be true unless a true hypothesis leads to a false conclusion. A truth table for pq is shown below. |
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INVERSE |
In many contexts in mathematics the term inverse indicates the opposite of something. This word and its derivatives are used widely inmathematics, as illustrated below. Inverse element of an element x with respect to a binary operation * with identity element e is an element y such that x * y = y * x = e. |
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CONTRAPOSITIVE |
The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then interchanging the resulting negations. In other words, thecontrapositive negates and switches the parts of the sentence. It does BOTH the jobs of the INVERSE and the CONVERSE. |
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LAW OF DETACHMENT |
In mathematical logic, the Law of Detachment says that if the following two statements are true: (1) If p, then q. (2) p. Then we can derive a third true statement: (3) q. |
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CONVERSE |
Switching the hypothesis and conclusion of a conditional statement. For example, the converse of "If it is raining then the grass is wet" is "If the grass is wet then it is raining." Note: As in the example, a proposition may be true but have a false converse |
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RULER POSTULATE |
Ruler Postulate Summary. On a number line, every point can be paired with a number and every number can be paired with a point. The number associated with a point A on a number line is called its coordinate. The distance between two point A and B is denoted by AB. (Note: there is NO line segment symbol!) |
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SEGMENT ADDITION POSTULATE |
The segment addition postulate is a fairly obvious-seeming postulate which states that: If a point B lies on a line segment , then . That is, the distance from one endpoint to the other is the sum of the distances from the middle point to either endpoint. |
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PROTRACTOR POSTULATE |
on line AB in a given plane, choose any point O between A and B. Consider ray OA and ray OB and all the rays that can be drawn from O on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: ray OA is paired with 0, and ray OB with 180, or, if ray OP is paired with X, and ray OQ with y, then angle POQ = l x-y l. |
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ANGLE ADDITION POSTULATE |
The angle addition postulate states that if B is in the interior of AOC, then. That is, the measure of the larger angle is the sum of the measures of the two smaller ones |
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CONDITIONAL |
Definition: A conditional statement, symbolized by p q, is an if-then statement in which p is a hypothesis and q is a conclusion. The logical connector in a conditional statement is denoted by the symbol . Theconditional is defined to be true unless a true hypothesis leads to a false conclusion. |
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ADDITION PROPERTY |
Definition: Additive Property of Equality. The additive property of equality states that if the same amount is added to both sides of an equation, then the equality is still true. |
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DISTRIBUTIVE PROPERTY |
In general, this term refers to the distributive property of multiplication which states that the. Definition: The distributive propertylets you multiply a sum by multiplying each addend separately and then add the products |
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SUBTRACTION PROPERTY |
Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal. For example: If 5 = 5, then 5 - 2 = 5 - 2. |
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DIVISION PROPERTY |
The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the sides remain equal |
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SUBSTITUTION PROPERTY |
Note: If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality. Thisproperty allows you to substitute quantities for each other into an expression as long as those quantities are equal |
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MULTIPLICATION PROPERTY |
The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal (i.e. equality is preserved). |
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REFLEXIVE PROPERTY OF EQUALITY, SYMMETRIC PROPERTY OF EQUALITY, TRANSITIVE PROPERTY OF EQUALITY. |
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CONGRUENCE OF SEGMENTS |
Congruent line segments are simply segments with the same measure (length). If segment AB is congruent to segment CD, we write: In geometrical figures, two segments are shown to be congruentby marking them with the same number of small perpendicular marks, as shown below. |
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CONGRUENCE OF ANGLES |
Angles are congruent if their measures, in degrees, are equal. Note: "congruent" does not mean "equal." While they seem quite similar,congruent angles do not have to point in the same direction. The only way to get equalangles is by piling two angles of equal measure on top of each other. |
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RIGHT ANGLES CONGRUENCE |
Theorem 1.7.3: If two angles are supplementary to the same angle (or to congruent angles, then the angles are congruent. Page 3.Theorem 1.7.4: Any two right angles are congruent. Given: ∠ABC is a right angle. |
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CONGRUENT SUPPLEMENTS |
(Proof): Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other. Given: Prove: Statements Reasons Page 3 October 16, 2012 (Proof): Congruent Supplements Theorem If 2 angles are supplementary to the same angle, then they are congruent to each other. |
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CONGRUENT COMPLEMENTS |
(Proof): Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other. Given: Prove: Statements Reasons Page 3 October 16, 2012 (Proof): Congruent Supplements Theorem If 2 angles are supplementary to the same angle, then they are congruent to each other. |
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LINEAR PAIR POSTULATE |
(Proof): Congruent Complements Theorem If 2 angles are complementary to the same angle, then they are congruent to each other. Given: Prove: Statements Reasons Page 3 October 16, 2012 (Proof): Congruent Supplements Theorem If 2 angles are supplementary to the same angle, then they are congruent to each other. |
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VERTICAL ANGLES CONGRUENCE |
Theorem: Vertical angles are always congruent. In the figure, 1 3 and 2 4. Proof: 1 and 2 form a linear pair, so by the Supplement Postulate, they are supplementary |
