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Geometric Proofs 27 October 2009
Geometric Proofs TWO COLUMN PROOFS FIVE KEY ELEMENTS  Given Diagrams Prove Statements Reasons
Reasons Given Information Definitions Postulates PROPERTIES Theorems
Given:  PROVE:      STATEMENTS					Reasons           1.   1. Given 2. Definition of supplementary angles 2.  3. Substitution Property 3.  4.  4. Subtraction Property 5.  5. Definition of Congruent Angles
Given:  Prove:  B 1 2 3 A C
Statements 				Reasons 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8. Given Definition of Right Angle Angle Addition Postulate Substitution Property (Steps 2 and 3) Given Definition of Congruent Angles Substitution Property (Step 4 and 6) Definitions of Complementary Angles
Given:  Prove:  A X 45˚ B C
QUIZ What is always the first step of a proof? Name 5 key elements of a proof. Name 5 types of reasons one can use during a proof. Measures __________: Angles and Segments are ______________. What is the last statement in a proof?
Statements 				Reasons 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 2. 3. 4. 5. 6. 7. 8. 9. Given Definitions of Angle Bisector Definitions of Congruent Angles Given Substitution Property Angle Addition Postulate Substitution Property Simplify Definition of Right Angle
Given:  Prove:  C D A B E
Statements 				Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Given Given Given Definition of Midpoint ASA (Steps 1, 4, 2)
Given: Prove: 1 A D 2 B C
Statements				Reasons Converse of the Consecutive Interior Angles Theorem Given Perpendicular Transversal Theorem Given Definition of Supplementary Angles
Given: Prove: B D 1 2 3 4 A E C
Statements				Reasons Substitution Property 5. 6. Given 3. 2. Corresponding Angles Postulate 2. 3. Given 1. 1. Substitution Property 4. 5. Converse of Corresponding Angles Postulate 6. 4.
Given: Prove: Z Y X W
Statements				Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Segment Addition Postulate Substitution Property
Given: Prove: L M 4 5 O N
Statements				Reasons 1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6. Definition of Right Angle Substitution Property
Geometric Proofs

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Geometric Proofs

  • 1. Geometric Proofs 27 October 2009
  • 2. Geometric Proofs TWO COLUMN PROOFS FIVE KEY ELEMENTS Given Diagrams Prove Statements Reasons
  • 3. Reasons Given Information Definitions Postulates PROPERTIES Theorems
  • 4. Given: PROVE: STATEMENTS Reasons 1. 1. Given 2. Definition of supplementary angles 2. 3. Substitution Property 3. 4. 4. Subtraction Property 5. 5. Definition of Congruent Angles
  • 5. Given: Prove: B 1 2 3 A C
  • 6. Statements Reasons 1. 2. 3. 4. 5. 6. 7. 8. 1. 2. 3. 4. 5. 6. 7. 8. Given Definition of Right Angle Angle Addition Postulate Substitution Property (Steps 2 and 3) Given Definition of Congruent Angles Substitution Property (Step 4 and 6) Definitions of Complementary Angles
  • 7. Given: Prove: A X 45˚ B C
  • 8. QUIZ What is always the first step of a proof? Name 5 key elements of a proof. Name 5 types of reasons one can use during a proof. Measures __________: Angles and Segments are ______________. What is the last statement in a proof?
  • 9. Statements Reasons 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 2. 3. 4. 5. 6. 7. 8. 9. Given Definitions of Angle Bisector Definitions of Congruent Angles Given Substitution Property Angle Addition Postulate Substitution Property Simplify Definition of Right Angle
  • 10. Given: Prove: C D A B E
  • 11. Statements Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Given Given Given Definition of Midpoint ASA (Steps 1, 4, 2)
  • 12. Given: Prove: 1 A D 2 B C
  • 13. Statements Reasons Converse of the Consecutive Interior Angles Theorem Given Perpendicular Transversal Theorem Given Definition of Supplementary Angles
  • 14. Given: Prove: B D 1 2 3 4 A E C
  • 15. Statements Reasons Substitution Property 5. 6. Given 3. 2. Corresponding Angles Postulate 2. 3. Given 1. 1. Substitution Property 4. 5. Converse of Corresponding Angles Postulate 6. 4.
  • 17. Statements Reasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Segment Addition Postulate Substitution Property
  • 18. Given: Prove: L M 4 5 O N
  • 19. Statements Reasons 1. 2. 3. 4. 5. 6. 1. 2. 3. 4. 5. 6. Definition of Right Angle Substitution Property