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**Geometry Proof: Proving Triangle Congruence** **Introduction:** The goal is to prove that triangles \(\triangle EFG\) and \(\triangle EHG\) are congruent given the angle information from the figure. --- **Given:** - \(\angle FEG = \angle HEG\) - \(\angle FGE = \angle HGE\) **To Prove:** - \(\triangle EFG \cong \triangle EHG\) **Proof:** | **Statements** | **Reasons** | |--------------------------------------|------------------------| | 1. \(\angle FEG = \angle HEG\) | 1. Given | | 2. \(\angle FGE = \angle HGE\) | 2. Given | | 3. \(\overline{EG} = \overline{EG}\) | 3. Reflexive property | | 4. \(\triangle EFG \cong \triangle EHG\) | 4. (Reason needed) | **Conclusion:** Therefore, \(\triangle EFG\) and \(\triangle EHG\) are congruent by the (selections needed). **Diagram Explanation:** The diagram shows a quadrilateral \(EFGH\) with diagonal \(EG\). The given angles are marked to illustrate the given equalities between them, which aids in proving the congruence of \(\triangle EFG\) and \(\triangle EHG\). **Note to Students:** To complete the proof, identify the correct congruence criterion (such as ASA, SSS, SAS, etc.) and fill in the missing reason in the proof table.

**Geometry Proof: Proving Triangle Congruence** **Introduction:** The goal is to prove that triangles \(\triangle EFG\) and \(\triangle EHG\) are congruent given the angle information from the figure. --- **Given:** - \(\angle FEG = \angle HEG\) - \(\angle FGE = \angle HGE\) **To Prove:** - \(\triangle EFG \cong \triangle EHG\) **Proof:** | **Statements** | **Reasons** | |--------------------------------------|------------------------| | 1. \(\angle FEG = \angle HEG\) | 1. Given | | 2. \(\angle FGE = \angle HGE\) | 2. Given | | 3. \(\overline{EG} = \overline{EG}\) | 3. Reflexive property | | 4. \(\triangle EFG \cong \triangle EHG\) | 4. (Reason needed) | **Conclusion:** Therefore, \(\triangle EFG\) and \(\triangle EHG\) are congruent by the (selections needed). **Diagram Explanation:** The diagram shows a quadrilateral \(EFGH\) with diagonal \(EG\). The given angles are marked to illustrate the given equalities between them, which aids in proving the congruence of \(\triangle EFG\) and \(\triangle EHG\). **Note to Students:** To complete the proof, identify the correct congruence criterion (such as ASA, SSS, SAS, etc.) and fill in the missing reason in the proof table.

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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**Geometry Proof: Proving Triangle Congruence** **Introduction:** The goal is to prove that triangles \(\triangle EFG\) and \(\triangle EHG\) are congruent given the angle information from the figure. --- **Given:** - \(\angle FEG = \angle HEG\) - \(\angle FGE = \angle HGE\) **To Prove:** - \(\triangle EFG \cong \triangle EHG\) **Proof:** | **Statements** | **Reasons** | |--------------------------------------|------------------------| | 1. \(\angle FEG = \angle HEG\) | 1. Given | | 2. \(\angle FGE = \angle HGE\) | 2. Given | | 3. \(\overline{EG} = \overline{EG}\) | 3. Reflexive property | | 4. \(\triangle EFG \cong \triangle EHG\) | 4. (Reason needed) | **Conclusion:** Therefore, \(\triangle EFG\) and \(\triangle EHG\) are congruent by the (selections needed). **Diagram Explanation:** The diagram shows a quadrilateral \(EFGH\) with diagonal \(EG\). The given angles are marked to illustrate the given equalities between them, which aids in proving the congruence of \(\triangle EFG\) and \(\triangle EHG\). **Note to Students:** To complete the proof, identify the correct congruence criterion (such as ASA, SSS, SAS, etc.) and fill in the missing reason in the proof table.
Transcribed Image Text:**Geometry Proof: Proving Triangle Congruence** **Introduction:** The goal is to prove that triangles \(\triangle EFG\) and \(\triangle EHG\) are congruent given the angle information from the figure. --- **Given:** - \(\angle FEG = \angle HEG\) - \(\angle FGE = \angle HGE\) **To Prove:** - \(\triangle EFG \cong \triangle EHG\) **Proof:** | **Statements** | **Reasons** | |--------------------------------------|------------------------| | 1. \(\angle FEG = \angle HEG\) | 1. Given | | 2. \(\angle FGE = \angle HGE\) | 2. Given | | 3. \(\overline{EG} = \overline{EG}\) | 3. Reflexive property | | 4. \(\triangle EFG \cong \triangle EHG\) | 4. (Reason needed) | **Conclusion:** Therefore, \(\triangle EFG\) and \(\triangle EHG\) are congruent by the (selections needed). **Diagram Explanation:** The diagram shows a quadrilateral \(EFGH\) with diagonal \(EG\). The given angles are marked to illustrate the given equalities between them, which aids in proving the congruence of \(\triangle EFG\) and \(\triangle EHG\). **Note to Students:** To complete the proof, identify the correct congruence criterion (such as ASA, SSS, SAS, etc.) and fill in the missing reason in the proof table.
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