Consider the diagram to the right below and complete the proof below. A E T E is the midpoint of AT m2OgE = m¿GOe Given: MLAEG > M2TEO0 Prove: GE = OE and AG > TO Statements Reasons 1. M2OGE = m2Goe 1. Given 2. GE = OE 2. 3. E is the midpoint of AT 3. Given 4. AE = ET | 4. Definition of the midpoint of a line segment. 5. AE = ET 5. Congruent segments have equal length. 6. MLAEG > m2teO 6. Given 7. AG > TO 7. A Isosceles Triangle Theorem, CPCTC B Definition of Isosceles Triangle; Triangle Inequality Theorem Converse of Isosceles Triangle Theorem; Hinge Theorem CPCTC, Triangle Inequality Theorem

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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Consider the diagram to the right below and complete the proof below.
A
E
T
Given:
E is the midpoint of AT
MLOGE = MLGOE
MLAEG > MLTEO
Prove:
GE = OE and AG > TO
Statements
Reasons
1. MLOGE = MLGOE
1. Given
2. GE = OE
2.
3. E is the midpoint of AT
3. Given
4. AE = ET
4. Definition of the midpoint of a line segment.
5. AE = ET
5. Congruent segments have equal length.
6. MLAEG > MLTEO
6. Given
7. AG > TO
7.
A
Isosceles Triangle Theorem, CPCTC
Definition of Isosceles Triangle; Triangle Inequality Theorem
Converse of Isosceles Triangle Theorem; Hinge Theorem
CPCTC, Triangle Inequality Theorem
Transcribed Image Text:Consider the diagram to the right below and complete the proof below. A E T Given: E is the midpoint of AT MLOGE = MLGOE MLAEG > MLTEO Prove: GE = OE and AG > TO Statements Reasons 1. MLOGE = MLGOE 1. Given 2. GE = OE 2. 3. E is the midpoint of AT 3. Given 4. AE = ET 4. Definition of the midpoint of a line segment. 5. AE = ET 5. Congruent segments have equal length. 6. MLAEG > MLTEO 6. Given 7. AG > TO 7. A Isosceles Triangle Theorem, CPCTC Definition of Isosceles Triangle; Triangle Inequality Theorem Converse of Isosceles Triangle Theorem; Hinge Theorem CPCTC, Triangle Inequality Theorem
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