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Given: 21 22; BG bisects LABF. CE bisects FCD. Prove: 23 24 A G B F N с D

Given: 21 22; BG bisects LABF. CE bisects FCD. Prove: 23 24 A G B F N с D

Elementary Geometry For College Students, 7e
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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**Problem Statement:** **Given:** - \( \angle 1 \cong \angle 2 \) - \( \overline{BG} \) bisects \( \angle ABF \) - \( \overline{CE} \) bisects \( \angle FCD \) **Prove:** \( \angle 3 \cong \angle 4 \) **Diagram Explanation:** The diagram illustrates a geometric configuration involving two intersecting lines \( \overline{AB} \) and \( \overline{CD} \). Points \( G, F, \) and \( E \) are positioned such that \( \overline{BG} \) and \( \overline{CE} \) bisect the given angles on the lines. The angles are labeled as follows: - \( \angle 1 \) is between \( \overline{AB} \) and \( \overline{BG} \) - \( \angle 2 \) is between \( \overline{BC} \) and \( \overline{CE} \) - \( \angle 3 \) is between \( \overline{GA} \) and \( \overline{AB} \) - \( \angle 4 \) is between \( \overline{CD} \) and \( \overline{EB} \) The goal is to prove that the measure of \( \angle 3 \) is congruent to the measure of \( \angle 4 \).
Transcribed Image Text:**Problem Statement:** **Given:** - \( \angle 1 \cong \angle 2 \) - \( \overline{BG} \) bisects \( \angle ABF \) - \( \overline{CE} \) bisects \( \angle FCD \) **Prove:** \( \angle 3 \cong \angle 4 \) **Diagram Explanation:** The diagram illustrates a geometric configuration involving two intersecting lines \( \overline{AB} \) and \( \overline{CD} \). Points \( G, F, \) and \( E \) are positioned such that \( \overline{BG} \) and \( \overline{CE} \) bisect the given angles on the lines. The angles are labeled as follows: - \( \angle 1 \) is between \( \overline{AB} \) and \( \overline{BG} \) - \( \angle 2 \) is between \( \overline{BC} \) and \( \overline{CE} \) - \( \angle 3 \) is between \( \overline{GA} \) and \( \overline{AB} \) - \( \angle 4 \) is between \( \overline{CD} \) and \( \overline{EB} \) The goal is to prove that the measure of \( \angle 3 \) is congruent to the measure of \( \angle 4 \).
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