What is the reason for #9? Given: ABCA where E is the midpoint of AC and D is the midpoint of BA Prove: DE|| BC and that BC = DE Statement Reason 1. Dis the midpoint of AB E is the midpoint of AC 2. MAD= mDB, MAE= MEB 1. 2. 3. mLA = mLA 3. 4. AD + DB = AB AE + EC = AC 5. AD + AD = AB AE + AE = AC 4. %3D 5. 6. 2(AD) = AB 2(AE)= AC | 6. Simplify AB AE = 2 7. Division AC 7. AD = 1 AE 2' AC 8. Division AD AB 2 9. ΔDAEΔΒAC 9. 10. = DE 10. вс 11. 11. DE =BC 12. MLADE = MLABC 12. %3D MLAED = MLACB 13. DE||BC 13.

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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What is the reason for #9?
Given: ABCA where E is the midpoint of AC and D is the midpoint of BA
Prove: DE|| BC and that BC = DE
B
Statement
Reason
1. Dis the midpoint of AB
E is the midpoint of AC
2. тAD- mDВ, тАЕ— тЕВ
1.
2.
3. mLA = mLA
3.
4. AD + DB = AB
AE + EC = AC
4.
5. AD + AD = AB
5.
AE + AE = AC
6. 2(AD) = AB
2(AE) = AC
6. Simplify
7. AD =
AB
AE =
2
AC
7. Division
AD
8.
АВ
_1 AE
1
8. Division
%3D
9. ΔDAE ~ΔΒAC
9.
DE
10.
вс
10.
11. DE =÷BC
11.
12. MLADE = MLABC
12.
MLAED = MLACB
13. DE||BC
13.
Transcribed Image Text:What is the reason for #9? Given: ABCA where E is the midpoint of AC and D is the midpoint of BA Prove: DE|| BC and that BC = DE B Statement Reason 1. Dis the midpoint of AB E is the midpoint of AC 2. тAD- mDВ, тАЕ— тЕВ 1. 2. 3. mLA = mLA 3. 4. AD + DB = AB AE + EC = AC 4. 5. AD + AD = AB 5. AE + AE = AC 6. 2(AD) = AB 2(AE) = AC 6. Simplify 7. AD = AB AE = 2 AC 7. Division AD 8. АВ _1 AE 1 8. Division %3D 9. ΔDAE ~ΔΒAC 9. DE 10. вс 10. 11. DE =÷BC 11. 12. MLADE = MLABC 12. MLAED = MLACB 13. DE||BC 13.
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