Geometry Chapter 2
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51 terms
Terms | Definitions |
|---|---|
 Points | Through any two _______ there exists exactly one line. |
| line | A _____ contains at least two points. |
| exactly one | If two lines intersect, then their intersection is ______ _______ point. |
| three | Through any _______ noncollinear points there exists exactly one plane. |
| non collinear | A plane contains at least three ___________ points. |
| plane | If two points lie in a plane, then the line containing them lies in the ________. |
| planes | If two _________ intersect, then their intersection is a line. |
| Addition Property | If a=b, then a+c=b+c. |
| Subtraction Property | If a=b, then a-c=b-c. |
| Multiplication Property | If a=b, then ac=bc. |
| Division Property | If a=b and c≠0, then a/c=b/c. |
| Substitution Property | If a=b, then a can be substituted for b in any equation or expression. |
| Distributive Property | a(b+c)=ab+ac, where a, b, and c are real numbers. |
| Reflexive Property | --Real Numbers--For any real number a, a=a. --Segment Lengths--For any segment, line segment AB, AB=AB --Angle Measure-- For any angle <A, m<A=m<A |
| Symmetric Property | --Real Numbers-- For any real numbers a and b, if a=b, then b=a --Segment Length-- For any segments _-AB-_ and _-CD-_, if AB=CD, then CD=AB --Angle Measure-- For any angles <A and <B, if m<A=m<B, then m<B=m<A |
| Transitive Property | --Real Numbers-- For any real numbers a, b, and c,if a=b and b=c, then a=c --Segment Length-- For any segments _-AB-_, _-CD-_, and _-EF-_, if AB=CD, and CD=EF, then AB=EF. --Angle Measure-- For any angles <A, <B, and <C, if m<A=m<B and m<B=m<C, then m<A=m<C |
| Conjecture | An unproven statement that is based on observations. EXAMPLE: Conjecture: All prime numbers are odd. Educated guess |
| Inductive Reasoning | The process of arriving at a conclusion based on a set of observations or examples EXAMPLE: Given the number pattern 1,5,9,13,..., you can use inductive reasoning to determine that the next number in the pattern in 17. |
| Counterexample | A specific case that shows a conjecture is false. EXAMPLE: All prime numbers are odd. Counterexample: 2, a prime number that is not odd. |
| Conditional Statement | A logical statement that has two parts, if/then |
| Hypothesis | It's what logically comes first after the "if". The "p" of a conditional statement. |
| Conclusion | It is what logically comes second after the "then". The "q" of a conditional statement. |
| Negation | Opposite ( ~ ) |
| Converse | If q, then p. |
| Inverse | If ~p, then ~q. |
| Contrapositive | If ~q, then ~p. |
| Logically Equivalent Statements | Two statements that are both True or both False. They both have the same truth value. |
| Perpendicular Lines | Lines that intersect at 90 degrees |
| Angle Congruence Postulate | Two angles are congruent if and only if their measures are equal. |
| Segment Congruence Postulate | Two segments are congruent if and only if they have the same length. |
| Supplement Theorem | If two angles form a linear pair, then they are supplementary. |
| Ray | One endpoint and all the points of the line on the one side of the endpoint. EXAMPLE: Ray AB (The endpoint is always listed first.) |
| Opposite Rays | Two collinear rays with the same endpoint. EXAMPLE: Ray AB and Ray AC (The endpoints are the same, ray go in opposite directions.) |
| Definition of Right Angles | If Angle 1 is a right angle then m Angle 1= 90 degrees |
| Definition of Perpendicular Lines | If Line l is perpendicular to line k, then m<1=m<2=m<3=m<4=90 |
| Definition of Supplementary Angles | If m<1+m<2 = 180 then <1 is supp. to <2 |
| Definition of Complementary Angles | If m<1+m<2 = 90 then, <1 is comp. to <2 |
| Definition of Congruent Angles | If <1 is congruent to <2 then m<1=m<2 |
| Definition of Segment Bisector | If AB bisects XY at A then XA=AY |
| Definition of Angle Bisector | If BD bisects <ABC then m<ABD=m<DBC |
| Definition of a Midpoint | If M is the midpoint of AB then AM=MB |
| Two angles supplementary to the same angle or to congruent angles are congruent | If <1 supp. <2 and <2 supp. <3 then <1 is congruent <3 |
| Two angles complementary to the same angle or to congruent angles are congruent | If <1 comp. <2 and <2 comp. <3 then <1 is congruent <3 |
| All right angles are congruent | If <1 and <2 are right angles then <1 is congruent <2 |
| Vertical Angles are Congruent | If Angle 1 is opposite to angle 2 then <1 is congruent <2 |
| Angle Addition Postulate | m<ABD+m<DBC= m<ABC |
| Segment Addition Postulate | XY+YZ=XZ |
| Linear Pair Postulate | If <1 and <2 are adjacent and supplementary then m<1+m<2=180 |
| Theorem | A statement that must be proved using undefined terms, definitions, postulates or other proven theorems |
| Postulate | A statement that is widely accepted without proof. |
| Deductive Reasoning | The process by which a person makes conclusions based on previously known facts, definitions, or rules. |
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