Given: E is the midpoint of AC, DE = ECProve: DE= AEDStatementsReasons1. E is the midpoint of AC1.2.2. Definition of Midpoint3.3. Given4. AE = DE4.5.5. Definition of Congruence6. DE = AE6.Given: RS =-RTT.RSProve: S is the midpoint of RTStatementsReasonsRT1. RS =1.2. 2RS = RT2.3.3. Segment Addition Postulate4. 2RS = RS + ST4.5. RS = ST5.6.6. Definition of MidpointGiven: Mis the midpoint of LN ,N is the midpoint of MO6,MNProve: LM NOStatementsReasons1. Mis the midpoint of LN1.2. LM = MN2. Definition of Midpoint3.3. Given4. MN = NO4.5.5. Transitive Property of Equality6.6. Definition of CongruenceO Gina il

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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.

Chapter1: Line And Angle Relationships

Section1.1: Early Definitions And Postulates

Problem 34E: Generalize your findings in Exercise 33. 33. Can you use the construction for the midpoint of a...

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Question

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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

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