1 / 13

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 .

britanni-rogers
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related