Practice for Proofs of: Parallel Lines Proving Converse of AIA, AEA, SSI, SSE By Mr. Erlin Tamalpais High School 10/20/09

Statement Reason 1)  4   5 2)  4 &  5 are alt interior angles 3)  1 &  4 are vertical angles 4)  1   4 5)  1   5 6)  1 &  5 are Corresponding Angles 7)r is a transversal over p, q 8)p is parallel to q 1)Given 2)Given/Definition of AlA 3)Definition of Vertical Angles 4)If Vertical Angles, then  5)Transitive Prop  6)Definition of Corresponding Angles. 7)Given/Definition of Transversal 8) If lines cut by a transversal form corresponding angles that are , then lines are parallel 11 22 33 44 55 66 Given: Prove: p is parallel to q QED p q r 77 Converse of Alternate Interior Angles Theorem 88 &  4   5

Statement Reason 1)  1   8 2)  1 &  8 are alt exterior angles 3)  1 &  4 are vertical angles 4)  1   4 5)  4   1 6)  4   8 7)  4 &  8 are Corresponding Angles 8)r is a transversal over p, q 9)p is parallel to q 1)Given 2)Given/Definition of AEA 3)Definition of Vertical Angles 4)If Vertical Angles, then  5)Symmetric Prop  6)Transitive Prop of  7)Definition of Corresponding Angles. 8)Given/Definition of Transversal 9) If lines cut by a transversal form corresponding angles that are , then lines are parallel 11 22 33 44 55 66 Given: Prove: p is parallel to q QED p q r 77 Converse of Alternate Exterior Angles Theorem 88 &  1   8

Statement Reason 1)r is a transversal to p, q 2)  3 &  5 are Supplementary 3)m  3 + m  5= 180 4)  3 and  1 form a Linear Pair 5)  3 &  1 are Supplementary 6)m  3 + m  1 = 180 7)m  3 +m  5 = m  3 + m  1 8)m  5=m  1 9)  5  1 10)  5 &  1 are Corresponding  s 11) p is parallel to q 1)Given 2)Given 3)Definition of Supplementary 4)Definition of Linear Pair 5)If Linear Pair, then Supplementary 6)Definition of Supplementary 7)Substitution Prop. of Equality 8)Subtraction Prop. of Equality 9)Definition of Congruent Angles 10)Definition of Corresponding  s 11)If then 11 22 33 44 55 66 Given: Prove: Line p is parallel to line q QED p q r Converse of Same Side Interior Angles are Supplementary and:  3 &  5 are supplementary transversal corresponding congruent lines are parallel.

Statement Reason 1)R is a transversal to P, Q 2)  1 &  7 are Supplementary 3)m  1 + m  7= 180 4)  3 and  1 form a Linear Pair 5)  3 &  1 are Supplementary 6)m  3 + m  1 = 180 7)m  1 +m  7 = m  3 + m  1 8)m  7=m  3 9)  7  3 10)  7 &  3 are Corresponding  s 11) P is parallel to Q 1)Given 2)Given 3)Definition of Supplementary 4)Definition of Linear Pair 5)If Linear Pair, then Supplementary 6)Definition of Supplementary 7)Substitution Prop. of Equality 8)Subtraction Prop. of Equality 9)Definition of Congruent Angles 10)Definition of Corresponding  s 11)If then 11 22 33 44 55 66 Given: Prove: Line p is parallel to line q QED p q r Converse of Same Side Exterior Angles are Supplementary and:  1 &  7 are supplementary transversal corresponding congruent lines are parallel. 77