University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2020
Views:

87

Pages:

2
Author:

Kasazami2c24

Geometry / Trig 2 Name __________________________ 3.2 Parallel Lines & Proofs Practice Date ___________________________ Proof #1 Proof of Alternate Exterior Angles congruent: Given: Prove: l || m 1  3 Statements t 1 l 2 m 3 Reasons 1. _____________________ 2. 1  2 1. ______________________________ 2. ______________________________ 3. _____________________ 3. If lines are parallel, then corresponding angles are congruent. 4. _____________________ 4. _____________________________ t Proof #2 1 Proof of Same-Side Exterior Angles supplementary: Given: l || m Prove: 1 is supplementary to 3 m 3 Statements 1. ________________________________ 2. ______ + ______ = 180 3. m2 = m3; 2  3 l 2 Reasons 1. 2. _________________________________ Angle Addition Postulate 3. _________________________________ _________________________________ _________________________________ 4. ______ + ______ = 180 4. _________________________________ 5. ________________________________ 5. Definition of _______________________ Proof #3 t Given: k || l Prove: 1 is supplementary to 7 2 1 4 3 Statements 1. 2. _______________________________ 1  ____ ; ______ = ______ 1. 6 5 8 7 k l _________________________________ 2. If lines are parallel, then alternate interior angles are congruent. 3. _______________________________ 3. Angle Addition Postulate 4. _______________________________ 4. Substitution 5. _______________________________ 5. _________________________________ Geometry / Trig 2 3.2 Properties of Parallel Lines & Proofs Proof #4 a Given: a || b ; c || d Prove: 6  11 1 9 13 b 2 5 3 6 10 7 11 14 a || b 2. 6  8 4 c 8 12 15 d 16 Statements 1. Homework Reasons 1. ____________________________________ 2. ____________________________________ ____________________________________ 3. _______________________ 3. Given 4. _______________________ 4. If lines are parallel, then alternate interior angles are congruent. 5. _______________________ 5. ____________________________________ Proof #5 a Given: a || b ; c || d Prove: 4 is supplementary to 9 1 5 9 13 Statements 1. ________________________________ 2. 4  ___ 3. ___  ___ b 2 6 10 14 3 7 11 15 12 16 4 8 c d Reasons 1. Given 2. Vertical Angles Theorem 3. _________________________________ _________________________________ _________________________________ 4. 4  5; m4 = m5 4. _________________________________ 5. ________________________________ 5. 6. 6. If lines are parallel, then ______________ 5 and 9 are supplementary Given _________________________________ 7. ________________________________ 7. Definition of supplementary angles 8. ________________________________ 8. _________________________________ 9. ________________________________ 9. Definition of _______________________