What is the reason for #6?

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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Question
What is the reason for #6?
Given: DE||BC
Prove: AD AE
DB EC
B
Statement
Reason
1. DE||BC
1.
2. mLA = m2A
2.
3. MLAED = MLACB
3.
4. ΔACB ~ΔΑED
4.
AD
5.
AB
AE
5.
%3D
EC
6. AD + DB = AB
6.
AE + EC = AC
AD
7.
AD+DB
AE
7.
AE+EC
8. AD(AE + EC) = AE(AD + DB)
8.
9. AD · AE + AD · EC = AE · AD + AE · DB
9.
10. AD · EC = AE · DB
10.
AD
11.
DB
AE
11.
%3D
EC
Transcribed Image Text:What is the reason for #6? Given: DE||BC Prove: AD AE DB EC B Statement Reason 1. DE||BC 1. 2. mLA = m2A 2. 3. MLAED = MLACB 3. 4. ΔACB ~ΔΑED 4. AD 5. AB AE 5. %3D EC 6. AD + DB = AB 6. AE + EC = AC AD 7. AD+DB AE 7. AE+EC 8. AD(AE + EC) = AE(AD + DB) 8. 9. AD · AE + AD · EC = AE · AD + AE · DB 9. 10. AD · EC = AE · DB 10. AD 11. DB AE 11. %3D EC
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