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

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

Statement Reason QED Prove: 4  5 Alternate Interior Angles are  Given: Alternate Interior Angles are  1 2 p 3 4 Prove: 4  5 5 6 Statement Reason 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 Definition of _____________ Angles If ______ then _______ Definition of ______ Angles If Vertical Angles, then  Symmetric Prop  Transitive Prop  QED

Statement Reason QED Prove: 4  5 Alternate Interior Angles are  Given: Alternate Interior Angles are  1 2 p 3 4 Prove: 4  5 5 6 Statement Reason 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 Definition of _____________ Angles If ______ then _______ Definition of ______ Angles If Vertical Angles, then  Symmetric Prop  Transitive Prop  5 Corresponding parallel transversal corresponding angles are congruent 1 Vertical 1  4 1 4 5 QED

Statement Reason QED Prove: 3  6 Alternate Interior Angles are  l Given: Alternate Interior Angles are  2 l 3 Prove: 3  6 6 Statement Reason 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 Definition of _____________ Angles If ______ then _______ Definition of ______ Angles If Vertical Angles, then  Transitive Prop  Symmetric Prop  QED

Statement Reason QED Prove: 3  6 Alternate Interior Angles are  l Given: Alternate Interior Angles are  2 l 3 Prove: 3  6 6 Statement Reason 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 Definition of _____________ Angles If ______ then _______ Definition of ______ Angles If Vertical Angles, then  Transitive Prop  Symmetric Prop  2 Corresponding parallel transversal corresponding angles are congruent Vertical 2 2 3 3 3 6 QED

Statement Reason QED Prove: 1  8 Alternate Exterior Angles are  Given: 1 2 p 3 4 Prove: 1  8 5 6 Statement Reason 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 Definition of Corresponding Angles If then Definition of Vertical Angles If Vertical Angles, then  Transitive Prop  parallel transversal corresponding angles are congruent QED

Statement Reason QED Prove: 1  8 Alternate Exterior Angles are  Given: 1 2 p 3 4 Prove: 1  8 5 6 Statement Reason 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

Statement Reason QED Prove: 3 & 5 are supplementary Same Side Interior Angles are Supplementary Given: 1 2 Prove: 3 & 5 are supplementary p 3 4 5 6 Statement Reason 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 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 parallel transversal corresponding angles are congruent QED

Statement Reason QED Prove: 3 & 5 are supplementary Same Side Interior Angles are Supplementary Given: 1 2 Prove: 3 & 5 are supplementary p 3 4 5 6 Statement Reason 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 parallel transversal corresponding angles are congruent QED

Statement Reason QED Prove: 6 & 4 are supplementary Same Side Interior Angles are Supplementary Given: 2 Prove: 6 & 4 are supplementary l 4 m 6 Statement Reason 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

Statement Reason QED Prove: 6 & 4 are supplementary Same Side Interior Angles are Supplementary Given: 2 Prove: 6 & 4 are supplementary l 4 m 6 Statement Reason 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 ___________ transversal Given _________ ______ 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 _________ 6 2 angles are _________ congruent corresponding Linear Pair Linear Pair 2 4 supplementary 180 Definition Substitution Supplementary QED

Statement Reason QED Prove: 3 & 5 are supplementary Same Side Interior Angles are Supplementary Given: 1 2 Prove: 3 & 5 are supplementary p 3 4 5 6 Statement Reason q ________________ 1 and 5 are ______________________ _______________ 3 and 1 are ___________ 3 & 1 are _____________ m3 + m1 = _______ m1 = m_____ ___________= 180 ______________________ 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 parallel transversal corresponding angles are congruent QED