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45 Cards in this Set

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 Postulate 1 (line) Two Points determine a line (p61) Postulate 2 (plane) Three noncollinear points determine a plane. (p61) Theorem: The Pythagorean Theorem The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides (p65) Theorem: The Triangle Angle Sum Theorem. The sum of the angles of a triangle is 180 degrees. (p.66) Theorem: Diameter of a circle If the diameter of a circle is "d", its circumference is pi(d) (p66) Theorem: Radius of a circle If the radius of a circle is "r", its area is pi times r squared. Postulate 3: The Ruler Postulate. The points on a line can be numbered so that positive number differences measure distances. (p85) Postulate 4: The Protractor Postulate The rays in a half-rotation can be numbered from 0 to 180 so that positive number differences measure angles. (p92) Theorem 1: The Betweenness of Points Theorem. If A-B-C, THEN AB+BC=AC. (p86) Theorem 2: The Betweenness of Rays Theorem. If 0A-0B-OC, then Angle AOB + ANGLE BOC = ANGLE AOC. (p93) Theorem 3: Complements of the same angle Complements of the same angle are equal (p106) Theorem 4: Supplements of the same angle Supplements of the same angle are equal. Theorem 5: The angles in a linear pair The angles in a linear pair are supplementary. (p111) Theorem 7: Perpendicular lines form... Perpendicular lines form right angles. (p118) Theorem 6: Vertical angles Vertical angles are equal. (p112) Corollary to the Ruler Postulate A line segment has exactly one midpoint. (p99) Corollary to the Protractor Postulate. An angle has exactly one ray that bisects it. (p100) Corollary to the definition of a right angle. All right angles are equal. (p118) Theorem 8: If the angles in a linear pair are equal... If the angles in a linear pair are equal, then their sides are perpendicular. Definition: Supplementary Two angles are supplementary iff their sum is 180 degrees. Each angle is called the SUPPLEMENT of the other. Definition: Complementary Two angles are complementary iff their sum is 90 degrees. Each angle is called the COMPLEMENT of the other. What is a corollary? A corollary is a theorem that can be easily proved as a consequence of a postulate or another theorem. Definition: midpoint of a line segment A point is the midpoint of a line segment iff it divides the line segment into two equal segments. Definition: bisects an angle A line bisects an angle iff it divides the angle into two equal angles. Congruent coinciding exactly when superimposed. Definition: (Betweeness of Points) A point is between two other points on the same line iff its coordinate is between their coordinates. ( A-B-C iff ab>c.) The Reflexive Property a = a (Any number is equal to itself) The Substitution Property If a = b, then a can be substituted for b in any expression. The Addition Property If a = b, then a + c = b + c. The Subtraction Property If a = b,then a - c = b - c The Multiplication Property If a = b, then ac = bc The Division Property If a = b and c does NOT = 0, then a divided by c = b divided by c. The Distributive Rule relates the operations of multiplication and addition. For any numbers a, b, and c, a(b + c) = ab + ac a(b - c) = ab - ac Postulate A postulate is a statement that is assumed to be true without proof. Direct proof If a, then b. If b, then c. If c, then d. Therefore, if a, then d. Indirect proof Suppose not d is true. If not d, then e If e, then f, and so on, until we come to a contradiction. Therefore, not d is false; so d is true. Syllogism A syllogism is an argument of the form If a then b If b then c Therefore, if a then c. Conditional statements A conditional statement consists of two clauses, one of which begins withthe work "if" or "when" or some equivalent word. Hypothesis If a, then b. The letter a represtns the "if" clause, or hypothesis. Conclusion If a, then be. The letter b represents the "then" clause, or conclusion. (The word "then" is often omitted.) Converse The converse of a conditional statement is found by interchanging the hypothesis and conclusion. The converse of "if a then b" is "if b then a" Is the converse always true? The converse may or may not be true, however the converse of a definition is always true. Theorem A theorem is a statement that is proved by reasoning deductively from already accepted statements. Premises of the argument The statements "if a then b, if b then c, ...." Conclusion of the argument If a then n. The conclution might be considered a theorem.