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14. Which method can you use to prove that the triangles are congruent? E %23 %23 A B

14. Which method can you use to prove that the triangles are congruent? E %23 %23 A B

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 Congruence Methods: Educational Exercise** ### Problem Statement: **14. Which method can you use to prove that the triangles are congruent?** The problem presents two triangles and asks to identify the correct method to prove their congruence. The options provided are: - **SSS (Side-Side-Side)** - **ASA (Angle-Side-Angle)** - **SAS (Side-Angle-Side)** - **AAS (Angle-Angle-Side)** #### Diagrams Description: The image shows two triangles labeled \( \triangle ABC \) and \( \triangle DEF \). - **\( \triangle ABC \)**: - This triangle has markings indicating: - Side \( AB \) is congruent to side \( DF \). - Side \( AC \) is congruent to side \( DE \). - Angle \( A \) is congruent to Angle \( D \). - **\( \triangle DEF \)**: - This triangle has the same markings as \( \triangle ABC \), indicating the congruence relationships between the corresponding sides and the angle. ### Required Response: To determine the congruence method based on the provided options and the diagram: 1. **SSS (Side-Side-Side)**: This method is used if all three sides of one triangle are congruent to all three corresponding sides of another triangle. 2. **ASA (Angle-Side-Angle)**: This method is used if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. 3. **SAS (Side-Angle-Side)**: This method is used if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. 4. **AAS (Angle-Angle-Side)**: This method is used if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle. Based on the diagram, two sides and the included angle are marked as congruent. Therefore, the correct method to prove congruence of these triangles is: - **SAS (Side-Angle-Side)** --- **Additional Question:** **8. Which line is perpendicular to line AB?** This question was not the focus based on the image, but implies understanding perpendicularity in geometric
Transcribed Image Text:--- **Geometry Congruence Methods: Educational Exercise** ### Problem Statement: **14. Which method can you use to prove that the triangles are congruent?** The problem presents two triangles and asks to identify the correct method to prove their congruence. The options provided are: - **SSS (Side-Side-Side)** - **ASA (Angle-Side-Angle)** - **SAS (Side-Angle-Side)** - **AAS (Angle-Angle-Side)** #### Diagrams Description: The image shows two triangles labeled \( \triangle ABC \) and \( \triangle DEF \). - **\( \triangle ABC \)**: - This triangle has markings indicating: - Side \( AB \) is congruent to side \( DF \). - Side \( AC \) is congruent to side \( DE \). - Angle \( A \) is congruent to Angle \( D \). - **\( \triangle DEF \)**: - This triangle has the same markings as \( \triangle ABC \), indicating the congruence relationships between the corresponding sides and the angle. ### Required Response: To determine the congruence method based on the provided options and the diagram: 1. **SSS (Side-Side-Side)**: This method is used if all three sides of one triangle are congruent to all three corresponding sides of another triangle. 2. **ASA (Angle-Side-Angle)**: This method is used if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. 3. **SAS (Side-Angle-Side)**: This method is used if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle. 4. **AAS (Angle-Angle-Side)**: This method is used if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle. Based on the diagram, two sides and the included angle are marked as congruent. Therefore, the correct method to prove congruence of these triangles is: - **SAS (Side-Angle-Side)** --- **Additional Question:** **8. Which line is perpendicular to line AB?** This question was not the focus based on the image, but implies understanding perpendicularity in geometric
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