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

2020
Views:

246

Pages:

2
Author:

Corey Garrison

Geometry/Trig 2 3.2 Parallel Lines & Proofs Homework Proof #1 Proof of Alternate Exterior Angles congruent: Given: Name Date 1 m Prove: Statements 1. L ||m 1. Given 2 2. angle 1 equiv angle2 3. angle 2 cong angle3 3 4. 41 hat = 43 4. Substitution Proof #2 Proof of Same-Side Exterior Angles supplementary: Given: Prove: 41 is supplementary to angle 3 Statements 1. 1. Given 2. m < 1 + m < 2 = 180 2. Angle Addition Postulate 3. m angle2=m angle3; angle2 equiv angle3 3. If line are parallel, then Corresponding angles are Reasons 2. Vertical Angles ure Congvent 3. If lines are parallel, then corresponding angles are congruent. 2 3 Reasons Congruent Substitution 4 5. Definition of Supplementary angles 4. mcl + ma3 = 180 5. 41 is supplementing to 23 Proof #3 Given: k||/ Prove: angle 1 is supplementary to angle 7 Statements 1. KIL 1. Given 2. = mc 8 3. m < 7 + m <= 8 = 180 3. Angle Addition Postulate 4. m < 7 + m < 1 = 180 4 Substitution 5. 21 is supplementing to 27 5. Definition of supplementeng A 2 6 1/5 8 3/7 2. If lines are parallel, then alternate interior angles are congruent. angle 1 cong angle Geometry/Trig 2 3.2 Properties of Parallel Lines & Proofs Homework Proof #4 b Given: Prove: a || b:cd 1/2 3/4 5 6 7/8 9/10 11/12 ← →d 13/14 15/16 Statements 1. 2. angle 6 equiv angle8 a || b 3. Al clld 4. 282211 5. angle 6 cong angle11 1. Given Reasons 2. If two lines are parallel, then Corresponding angles are congruent 3. Given 4. If lines are parallel, then alternate interior angles 5. are congruent. Substitution Proof #5 a Given: a || b; cd 1/2 1 3/4 Prove: 14 is supplementary to angle 9 5/6 7/8 9/10 11/12 →d 13/14 15/16 Reasons Statements 1. allb 1. Given 2. angle4 equiv angle 7 3. angle I= angle 5 2. Vertical Angles Theorem 3. If a two lines are. parallel, then corresponding congruent angle 4 cong angle5; m angle4=m angle5 4. Clld 5. angle 5 and angle 9 are supplementary 6. 7. m < 5 + m < 9 = 180 8. mc4 +mc9 = 180 9. <4 is supplementery to 19 4. Ongles ove Substitution 5. Given 6. If lines are parallel, then sare s-de interior angles are supplementery 7. Definition of supplementary angles 8. Substitution 9. Definition of Supplementary Angles angle 6 equiv angle11