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Complete this proof of Theorem 16. Civen: Transversal t intersects lines m and n; Z1 is supplementary to 2. 3 Prove: m ll n. 2. Proof Statements Reasons 1. Giver 1. Transversal t intersects lines m and n; Z1 is supplementary to 2. 2. 2. 3. 22 = 23. 3. Zs that are sup. of the same Z are E./P11Y 4. . m |l n. 4. If a trans. intersects two lines so that alt. int. are =, then the lines are |I. (T. 131

Complete this proof of Theorem 16. Civen: Transversal t intersects lines m and n; Z1 is supplementary to 2. 3 Prove: m ll n. 2. Proof Statements Reasons 1. Giver 1. Transversal t intersects lines m and n; Z1 is supplementary to 2. 2. 2. 3. 22 = 23. 3. Zs that are sup. of the same Z are E./P11Y 4. . m |l n. 4. If a trans. intersects two lines so that alt. int. are =, then the lines are |I. (T. 131

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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cisal ale supplementary, then the lines are parallel. Complete this proof of Theorem 16. Civen: Transversal t intersects lines m and n; 21 is supplementary to 2. m Prove: m ll n. 2. Proof Statements Reasons 1. Transversal t intersects lines m and n; 1. Giver Z1 is supplementary to 2. 2. 2. 3. 22 =23. 3. Zs that are sup. of the same Z are E.11! 4. . m |l n. 4. If a trans. intersects two lines so that alt. int. Zs are =, then the lines are II. (T.13) 20
Transcribed Image Text:cisal ale supplementary, then the lines are parallel. Complete this proof of Theorem 16. Civen: Transversal t intersects lines m and n; 21 is supplementary to 2. m Prove: m ll n. 2. Proof Statements Reasons 1. Transversal t intersects lines m and n; 1. Giver Z1 is supplementary to 2. 2. 2. 3. 22 =23. 3. Zs that are sup. of the same Z are E.11! 4. . m |l n. 4. If a trans. intersects two lines so that alt. int. Zs are =, then the lines are II. (T.13) 20
VWU 1navC prUVeu timat If twó lines are parallel, then the alternate exterior angles are congruent. Is converse of this true? If you study the proof of Theorem 14 on page 18, it will help you prove Theorem 15 Theorem 15: If a transversal intersects two lines so that alternate exterior angles are congruent, ther the lines are parallel. Complete this proof of Theorem 15. Given: Transversal t intersects lines m and n; L1 = 23. Prove: m ll n. 1. Proof Statements Reasons Tankerraleinterrede lino nads 1. Givcn 2. 2. 3. 4. If a trans, intersects two lines so that cor. Zs are =, then the lines are ll.0.14) 4. . Theorem 12 uses parallel lines to prove that interior angles on the same side of the transversal are sup mentary. To prove Theorem 16, we must prove either alternate interior, corresponding, or alternate ext angles are congruent. If we can do this, then we know the lines are parallel. side of th
Transcribed Image Text:VWU 1navC prUVeu timat If twó lines are parallel, then the alternate exterior angles are congruent. Is converse of this true? If you study the proof of Theorem 14 on page 18, it will help you prove Theorem 15 Theorem 15: If a transversal intersects two lines so that alternate exterior angles are congruent, ther the lines are parallel. Complete this proof of Theorem 15. Given: Transversal t intersects lines m and n; L1 = 23. Prove: m ll n. 1. Proof Statements Reasons Tankerraleinterrede lino nads 1. Givcn 2. 2. 3. 4. If a trans, intersects two lines so that cor. Zs are =, then the lines are ll.0.14) 4. . Theorem 12 uses parallel lines to prove that interior angles on the same side of the transversal are sup mentary. To prove Theorem 16, we must prove either alternate interior, corresponding, or alternate ext angles are congruent. If we can do this, then we know the lines are parallel. side of th
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