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2.5: Postulates and Proofs 2.6: Algebraic Proof

2.5: Postulates and Proofs 2.6: Algebraic Proof. Postulate : A statement that describes a fundamental relationship between the basic terms of Geometry. Postulates are accepted as true. Postulate 2.1 : Through any 2 points, there is exactly 1 line.

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2.5: Postulates and Proofs 2.6: Algebraic Proof

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  1. 2.5: Postulates and Proofs2.6: Algebraic Proof

  2. Postulate: A statement that describes a fundamental relationship between the basic terms of Geometry. Postulates are accepted as true. Postulate 2.1: Through any 2 points, there is exactly 1 line. Postulate 2.2: Through any 3 noncollinear points, there is exactly 1 plane. Postulate 2.3: A line contains at least 2 points. Postulate 2.4: A plane contains at least 3 noncollinear points.

  3. Postulate 2.5: If 2 points lie in a plane, then the entire line containing those points lies in the plane. B A

  4. Postulate 2.6: If 2 lines intersect, then their intersection is exactly one point. Postulate 2.7: If 2 planes intersect, then their intersection is a line.

  5. Proof: A logical argument in which each statement you make is supported by a statement that is accepted as true. Paragraph Proof: Informal proof. Your solution steps are written in paragraph form.

  6. Theorem: A statement that can be proven by undefined terms, definitions, and postulates. A M B

  7. Properties of Equality: Reflexive Property: a = a Ex. 3 = 3 Symmetric Property: If a = b, then b = a Ex. If 2+3 = 5, then 5 = 2+3. Transitive Property: If a = b and b = c, then a = c. Ex. If 2+3 = 5 and 5 = 4+1, then 2+3 = 4+1. Addition Property of Equality: If a = b, then a+c = b+c. Ex. If 2+3 = 5, then 2+3+4 = 5+4 Subtraction Property of Equality: If a = b, then a-c = b-c. Ex. If 2+3 = 5, then 2+3-4 = 5-4

  8. Substitution Property: If a = b, then “a” may be replaced by “b” in any expression. Distributive Property: a(b + c) = ab + ac. Ex. 3(x + 2) = 3x + 6

  9. Two-Column Proof: Formal proof. Statements Reasons 1. 2. 3. 4. 1. 2. 3. 4.

  10. Ex. Write a 2-column proof Statements Reasons

  11. Assignment: Section 2.5 Pg. 92 #s 16-27, 33-35 Section 2.6 Pg. 97 #s 14-24

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