Given: E is the midpoint of AC, DE = EC Prove: DE = AE

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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Given: E is the midpoint of AC, DE = EC
Prove: DE= AE
D
Statements
Reasons
1. E is the midpoint of AC
1.
2.
2. Definition of Midpoint
3.
3. Given
4. AE = DE
4.
5.
5. Definition of Congruence
6. DE = AE
6.
Given: RS =
-RT
T.
R
S
Prove: S is the midpoint of RT
Statements
Reasons
RT
1. RS =
1.
2. 2RS = RT
2.
3.
3. Segment Addition Postulate
4. 2RS = RS + ST
4.
5. RS = ST
5.
6.
6. Definition of Midpoint
Given: Mis the midpoint of LN ,
N is the midpoint of MO
6,
M
N
Prove: LM NO
Statements
Reasons
1. Mis the midpoint of LN
1.
2. LM = MN
2. Definition of Midpoint
3.
3. Given
4. MN = NO
4.
5.
5. Transitive Property of Equality
6.
6. Definition of Congruence
O Gina il
Transcribed Image Text:Given: E is the midpoint of AC, DE = EC Prove: DE= AE D Statements Reasons 1. E is the midpoint of AC 1. 2. 2. Definition of Midpoint 3. 3. Given 4. AE = DE 4. 5. 5. Definition of Congruence 6. DE = AE 6. Given: RS = -RT T. R S Prove: S is the midpoint of RT Statements Reasons RT 1. RS = 1. 2. 2RS = RT 2. 3. 3. Segment Addition Postulate 4. 2RS = RS + ST 4. 5. RS = ST 5. 6. 6. Definition of Midpoint Given: Mis the midpoint of LN , N is the midpoint of MO 6, M N Prove: LM NO Statements Reasons 1. Mis the midpoint of LN 1. 2. LM = MN 2. Definition of Midpoint 3. 3. Given 4. MN = NO 4. 5. 5. Transitive Property of Equality 6. 6. Definition of Congruence O Gina il
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