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Geometry CH 2
This set will help you to study definitions, properties and theorems from ch2.9
| Term | Definition |
|---|---|
| Inductive Reasoning | Using specific examples or patterns to make a general conclusion. |
| Conjecture | An educated guess or generalization based on observed patterns. |
| Counterexample | An example that proves a conjecture false. |
| Deductive Reasoning | Using facts, definitions, and accepted properties to make a logical conclusion. |
| Law of Detachment | If p → q is true and p is true, then q must be true. |
| Law of Syllogism | If p → q and q → r are true, then p → r is also true. |
| Statement | A sentence that is either true or false, not both. |
| Negation | The opposite of a statement. Example: “It is raining” → “It is not raining.” |
| Compound Statement | Two or more statements joined by the words “and” (∧) or “or” (∨). |
| Conjunction | A compound statement using “and” (∧); true only when both parts are true. |
| Disjunction | A compound statement using “or” (∨); true if at least one part is true. |
| Truth Table | A chart used to determine all possible truth values of a compound statement. |
| Conditional Statement | An “if-then” statement written as p → q. |
| Hypothesis | The “if” part of a conditional statement (p). |
| Conclusion | The “then” part of a conditional statement (q). |
| Converse | Switch the hypothesis and conclusion: q → p. |
| Inverse | Negate both the hypothesis and conclusion: ~p → ~q. |
| Contrapositive | Switch and negate both parts: ~q → ~p. |
| Biconditional Statement | A statement that combines a conditional and its converse using “if and only if.” |
| Logically Equivalent | Statements that always have the same truth value. |
| Venn Diagram | A diagram using circles to represent relationships among sets or statements. |
| Property of Equality | A rule that allows you to solve equations logically (addition, subtraction, multiplication, division, etc.). |
| Reflexive Property | a = a (any quantity is equal to itself). |
| Symmetric Property | If a = b, then b = a. |
| Transitive Property | If a = b and b = c, then a = c. |
| Substitution Property | If a = b, then a may replace b in any expression. |
| Addition Property of Equality | If a = b, then a + c = b + c. |
| Subtraction Property of Equality | If a = b, then a − c = b − c. |
| Multiplication Property of Equality | If a = b, then a·c = b·c. |
| Division Property of Equality | If a = b and c ≠ 0, then a ÷ c = b ÷ c. |
| Distributive Property | a(b + c) = ab + ac. |
| Algebraic Proof | A logical argument that uses properties of equality to show a statement is true. |
| Two-Column Proof | A proof with statements in one column and reasons in another. |
| Given | Statement you are asked to show is true. |
| Segment Addition Postulate | If B is between A and C, then AB + BC = AC. |
| Angle Addition Postulate | If point D is in the interior of ∠ABC, then m∠ABD + m∠DBC = m∠ABC. |
| Definition of Congruent Segments | Segments that have equal lengths. |
| Definition of Congruent Angles | Angles that have equal measures. |
| Midpoint | The point that divides a segment into two congruent segments. |
| Definition of Midpoint | If M is the midpoint of AB, then AM = MB. |
| Bisector | A line, ray, or segment that divides another figure into two equal parts. |
| Angle Bisector | A ray that divides an angle into two congruent angles. |
| Vertical Angles | Two non-adjacent angles formed by intersecting lines; they are congruent. |
| Linear Pair | Two adjacent angles whose non-common sides form a straight line (supplementary). |
| Complementary Angles | Two angles whose measures add up to 90°. |
| Supplementary Angles | Two angles whose measures add up to 180°. |
| Right Angle | An angle that measures exactly 90°. |
| Perpendicular Lines | Lines that intersect to form right angles. |
| Parallel Lines | Lines in the same plane that never intersect. |
| Transversal | A line that intersects two or more other lines in a plane. |
| Alternate Interior Angles | Non-adjacent interior angles on opposite sides of a transversal; congruent if lines are parallel. |
| Alternate Exterior Angles | Non-adjacent exterior angles on opposite sides of a transversal; congruent if lines are parallel. |
| Corresponding Angles | Angles in the same relative position; congruent if lines are parallel. |
| Same-Side Interior Angles | Interior angles on the same side of a transversal; supplementary if lines are parallel. |
| Proof | A logical argument that shows a statement is true using definitions, postulates, and previously proven theorems. |
| Complement Theorem | If two angles form a right angle, then they are complementary. |
| Linear Pair Theorem (Supplement Theorem) | If two angles form a linear pair, then the are supplementary |
| Congruent Complements Theorem | If two angles are complementary to the same angle, then they are congruent. (If ∠A is complementary to ∠B and ∠C is complementary to ∠B, then ∠A is congruent to ∠C.) |
| Congruent Supplements Theorem | If two angles are supplementary to the same angle, then they are congruent. (If ∠A is supplementary to ∠B and ∠C is supplementary to ∠B, then ∠A is congruent to ∠C.) |
Created by:
TJStudies
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