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

2020
Views:

56

Pages:

6
Author:

Beckett Gray

Geometry/Trig USING Parallel Line Proofs - Page 1 Name: Schrier Date: Fall 2015 1 1. Given: g//h and s // t Prove: 2/15 9 h 3/4 5/6 9/10 11/12 13/14 7/8 15 16 Statements Reasons 2 1. gh 3). st 4). 46215 5). 42215 S ), Griven 4.) if lines are parallel, then Corresponding angles are congruent. a), Given 4) if lines are parallel, then alternate interior angles are congruent. 5). Transitive 2. Given: k//m Prove: 21 is supplementary to 27 2/6 1/5 4/8 3/7 m k Statements Reasons 1) Given 2) mal=m23 DI if lines are parallel, then corresponding angles are congruent. 3) mcs+ m² 7 = 180 3). Ange Addition postulate 41. mai + m² 7=180 41. substitution. 5) 21 and 27 are supplementary 51. cufinition of oupplementary angles USING Parallel Line Proofs - Page 2 3. Given: vec CD // overleftrightarrow BE : angle 3 equiv angle1 Prove: BE bisects DBA C B 3 3 2 A 1 D E Statements Reasons 1) CBBE 1). Given 2) if lines are parallel, then alternate interior angies are congruent. 3). 4341 31. Given 4) 23 cong2 4). substitution 5), BE bisects LDBA 5). definition of an angie bisector A 4. Given: overleftrightarrow AD // vec BC ; angle 1 equiv angle2 Prove: AB bisects ∠CAD Statements Reasons 1) DEC 2). 23승 22 1). Given 3) angle 1 cong angle2 angle 1 cong angle3 5). AB bisects < CAD C 2 B 2) if lines are parallel, then alternate interior angies are congruent. 3). Given 41. Substitution 51. definition of an angle bisector D PROVING Parallel Line Proofs - Page 3 5. Given: angle 4 equiv angle13; // s Prove: h//g 9 1/2 3/4 9/10 11/12 h 5/6 13/14 7/8 15/16 Statements Reasons S 1t/s 1) Given 4) leftarrow B = - 13 2) if lines are parallel, then alternate interior angues are congruent. 3). angle 4 cong angle13 3). Given 4). angle 4 = angle8 4). transitive 5). //g 5). it corresponding angies are congruent, then lines are parallel C A 2 3 6. Given: overleftrightarrow AB | ∠CAD: angle 1 cong angle2 Prove: ADBC Statements Reasons D 1). AB bisects &CAD 2) - 1 cong< 3 3) 21522 4). L B cong L3 5). b/ BC 1. Given 2) definition of on angie bisector 31 Given 4). Transitive 5). If acternate unterior angles. are congruent, then lines are parallel.