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Practice for Proofs of: Parallel Lines Proving AIA, AEA, SSI, SSE only

Practice for Proofs of: Parallel Lines Proving AIA, AEA, SSI, SSE only. By Mr. Erlin Tamalpais High School 10/05/2010. Note: Blue slides match scaffolded notes handout. r. parallel transversal corresponding. angles are congruent. Given :. Alternate Interior Angles are .

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Practice for Proofs of: Parallel Lines Proving AIA, AEA, SSI, SSE only

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  1. Practice for Proofs of: Parallel LinesProving AIA, AEA, SSI, SSE only By Mr. Erlin Tamalpais High School 10/05/2010 Note: Blue slides match scaffolded notes handout

  2. r parallel transversal corresponding angles are congruent Given: Alternate Interior Angles are  Statement Reason 1 2 p 3 4 Prove: 4  5 5 6 q • p is parallel to q • r is a transversal to p, q • 1 and 5 are Corresponding Angles • 1  5 • 1 and 4 are Vertical Angles • 1  4 • 4  1 • 4  5 • Given • Given • Definition of Corresponding Angles • If then • Definition of Vertical Angles • If Vertical Angles, then  • Symmetric Prop  • Transitive Prop  QED

  3. r Given: Alternate Interior Angles are  Statement Reason 1 2 p 3 4 Prove: 4  5 5 6 q • p is parallel to q • r is a transversal to p, q • 1 and  ____ are Corresponding Angles • 1  5 • ____ and 4 are Vertical Angles • ____________ • 4  _______ • ___________ • Given • Given • Definition of _____________ Angles • If ______ then _______ • Definition of ______ Angles • If Vertical Angles, then  • Symmetric Prop  • Transitive Prop  QED

  4. r parallel transversal corresponding angles are congruent Given: Alternate Interior Angles are  Statement Reason 1 2 p 3 4 Prove: 4  5 5 6 q • p is parallel to q • r is a transversal to p, q • 1 and  ____ are Corresponding Angles • 1  5 • ____ and 4 are Vertical Angles • ____________ • 4  _______ • ___________ • Given • Given • Definition of _____________ Angles • If ______ then _______ • Definition of ______ Angles • If Vertical Angles, then  • Symmetric Prop  • Transitive Prop  5 Corresponding 1 Vertical 1  4 1 4 5 QED

  5. t Given: Alternate Interior Angles are  Statement Reason 2 l 3 Prove: 3  6 6 m • l is parallel to m • t is a transversal to l & m • 6 and  ____ are Corresponding Angles • 6  2 • ____ and 3 are Vertical Angles • _____ ______ • 6  _______ • ___________ • Given • Given • Definition of _____________ Angles • If ______ then _______ • Definition of ______ Angles • If Vertical Angles, then  • Transitive Prop  • Symmetric Prop  QED

  6. t parallel transversal corresponding angles are congruent Given: Alternate Interior Angles are  Statement Reason 2 l 3 Prove: 3  6 6 m • l is parallel to m • t is a transversal to l & m • 6 and  ____ are Corresponding Angles • 6  2 • ____ and 3 are Vertical Angles • _____ ______ • 6  _______ • ___________ • Given • Given • Definition of _____________ Angles • If ______ then _______ • Definition of ______ Angles • If Vertical Angles, then  • Transitive Prop  • Symmetric Prop  2 Corresponding Vertical 2 2 3 3 3 6 QED

  7. r parallel transversal corresponding angles are congruent Alternate Exterior Angles are  Given: Statement Reason 1 2 p 3 4 Prove: 1  8 5 6 q 7 8 • p is parallel to q • r is a transversal to p, q • 1 and 5 are Corresponding Angles • 1  5 • 5 and 8 are Vertical Angles • 5  8 • 1  8 • Given • Given • Definition of Corresponding Angles • If then • Definition of Vertical Angles • If Vertical Angles, then  • Transitive Prop  QED

  8. r Alternate Exterior Angles are  Given: Statement Reason 1 2 p 3 4 Prove: 1  8 5 6 q 7 8 • p is parallel to q • r is a transversal to p, q • 1 and 5 are Corresponding Angles • 1  5 • 5 and 8 are Vertical Angles • 5  8 • 1  8 • _________ • _________ • ________ of ____________ ________ • If then • __________ of _________ _________ • If ________, then ______ • _____________________ QED

  9. parallel transversal corresponding angles are congruent Same Side Interior Angles are Supplementary r Statement Reason Given: Prove: 3 &5 are supplementary 1 2 p 3 4 5 6 q • p is parallel to q • r is a transversal to p, q • 1 and 5 are Corresponding Angles • 1  5 • 3 and 1 are Linear Pair • 3 & 1 are Supplementary • m3 + m1 = 180 • m1 = m5 • m3 + m5= 180 • 3 & 5 are Supplementary • Given • Given • Definition of Corresponding Angles • If then • Definition of Linear Pair • If Linear Pair, then Supplementary • Definition of Supplementary (or if supplementary then 180) • Definition of Congruent Angles • Substitution Prop of Equality • Definition of Supplementary QED

  10. parallel transversal corresponding angles are congruent Same Side Interior Angles are Supplementary r Statement Reason Given: Prove: 3 &5 are supplementary 1 2 p 3 4 5 6 q • p is parallel to q • r is a __________ to p, q • 1 and 5 are _________________ Angles • ____  ____ • 3 and 1 are ________ • __ & __ are Supplementary • m3 + m1 = ______ • m1 = m5 • m3 + m5= 180 • 3 & 5 are ___________ • _________ • Given • __________ of Corresponding Angles • If then • Definition of ____________ • If Linear Pair, then ____________ • __________ of Supplementary • Definition of Congruent Angles • __________ Prop of Equality • Definition of Supplementary QED

  11. Same Side Interior Angles are Supplementary t Statement Reason Given: Prove: 6 &4 are supplementary 2 l 4 m 6 • l// m; t is a __________ to l & m • 6 & 2 are ___________ Angles • ____  ____ • m6 = m2 • 2 & 4 form ________ • __ & __ are Supplementary • m2 + m4 = ______ • m6 + m4= 180 • 6 & 4 are ___________ • _________ • ______ of Corresponding Angles • If then • Definition of Congruent Angles • Definition of ____________ • If Linear Pair, then ____________ • __________ of Supplementary • __________ Prop of Equality • Definition of Supplementary parallel transversal _________ angles are _________ QED

  12. Same Side Interior Angles are Supplementary t Statement Reason Given: Prove: 6 &4 are supplementary 2 l 4 m 6 transversal Given • l// m; t is a __________ to l & m • 6 & 2 are ___________ Angles • ____  ____ • m6 = m2 • 2 & 4 form ________ • __ & __ are Supplementary • m2 + m4 = ______ • m6 + m4= 180 • 6 & 4 are ___________ • _________ • ______ of Corresponding Angles • If then • Definition of Congruent Angles • Definition of ____________ • If Linear Pair, then ____________ • __________ of Supplementary • __________ Prop of Equality • Definition of Supplementary corresponding Defin. parallel transversal _________ angles are _________ congruent 6 2 corresponding Linear Pair Linear Pair supplementary 2 4 180 Definition Substitution Supplementary QED

  13. parallel transversal corresponding angles are congruent Same Side Interior Angles are Supplementary r Statement Reason Given: Prove: 3 &5 are supplementary 1 2 p 3 4 5 6 q • ________________ • ________________ • 1 and 5 are ______________________ • _______________ • 3 and 1 are ___________ • 3 & 1 are _____________ • m3 + m1 = _______ • m1 = m_____ • ___________= 180 • ______________________ • Given • Given • Definition of Corresponding Angles • If then • Definition of Linear Pair • If Linear Pair, then Supplementary • Definition of Supplementary • Definition of Congruent Angles • Substitution Prop of Equality • Definition of Supplementary QED

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