Examine the proof that follows. What is reason 2? Given: EBD LECB andm zECB = 45°

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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Examine the proof that follows. What is reason 2?
Given: EBD LECB andm ZECB = 45°
Prove: ZABE <DCE
Statement
Reason
1.
1. Given
2. AD is a straight line.
2.
3. ZABE and ZEBC are a linear 3. Definition of a linear pair
pair.
2DCE and ZECB are a linear
pair.
4.
4. Linear pairs are
supplementary.
5. m ZABE + m ZEBC = m
5. Substitution
ZDCE + m 2ECB
6.
6. Substitution
7. m ZABE = m ZDCE
7.
8. m ZABE =m ZDCE
8.
O Substitution
Transcribed Image Text:Examine the proof that follows. What is reason 2? Given: EBD LECB andm ZECB = 45° Prove: ZABE <DCE Statement Reason 1. 1. Given 2. AD is a straight line. 2. 3. ZABE and ZEBC are a linear 3. Definition of a linear pair pair. 2DCE and ZECB are a linear pair. 4. 4. Linear pairs are supplementary. 5. m ZABE + m ZEBC = m 5. Substitution ZDCE + m 2ECB 6. 6. Substitution 7. m ZABE = m ZDCE 7. 8. m ZABE =m ZDCE 8. O Substitution
pair
DCE and ECB are a linear
pair.
4. Linear pairs are
supplementary
5. m LABE+ m ZEBC = m
5. Substitution
ZDCE+ m ECB
6.
6. Substitution
7. m LABE= m ZDCE
7.
8. m ZABE m zDCE
8.
Substitution
m ZABE+ 45° = m ¿DCE + 45°
ZEBD ECB, m ¿ECB = 45°
O Two points make a straight line.
Transcribed Image Text:pair DCE and ECB are a linear pair. 4. Linear pairs are supplementary 5. m LABE+ m ZEBC = m 5. Substitution ZDCE+ m ECB 6. 6. Substitution 7. m LABE= m ZDCE 7. 8. m ZABE m zDCE 8. Substitution m ZABE+ 45° = m ¿DCE + 45° ZEBD ECB, m ¿ECB = 45° O Two points make a straight line.
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