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A Bo E D

A Bo E 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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For two triangles to be congruent, it is necessary to have congruent measures of 3 sets of corresponding parts with at least one set being corresponding sides.

The three congruency rules are called side-angle-side, angle-side-angle, and side-side-side. Given the two triangles below and the marked corresponding parts, is there enough information to determine if they are congruent? By which rule? Write a congruency statement relating the two triangles.

 

The image depicts two intersecting triangles, \( \triangle ABC \) and \( \triangle ADE \). The points \( A \), \( B \), \( C \), \( D \), and \( E \) are marked with red dots at each vertex. ### Key Features and Explanation: - **Triangles**: - \( \triangle ABC \) is formed by the points \( A \), \( B \), and \( C \). - \( \triangle ADE \) is formed by the points \( A \), \( D \), and \( E \). - **Intersection Point**: - The triangles intersect at point \( E \). - **Line Segments**: - The line segments \( BE \) and \( CD \) are marked with single hash lines, indicating they are equal in length. - Similarly, the line segments \( CE \) and \( DE \) are also marked with hash lines, suggesting they are equal in length to each other. - **Visual Representation**: - The diagram is a side view, suggesting equal line segments contribute to congruent triangles or particular geometric properties. This image can be used to demonstrate geometric concepts such as intersecting lines, congruent triangles, or other properties like parallel lines and transversal properties.
Transcribed Image Text:The image depicts two intersecting triangles, \( \triangle ABC \) and \( \triangle ADE \). The points \( A \), \( B \), \( C \), \( D \), and \( E \) are marked with red dots at each vertex. ### Key Features and Explanation: - **Triangles**: - \( \triangle ABC \) is formed by the points \( A \), \( B \), and \( C \). - \( \triangle ADE \) is formed by the points \( A \), \( D \), and \( E \). - **Intersection Point**: - The triangles intersect at point \( E \). - **Line Segments**: - The line segments \( BE \) and \( CD \) are marked with single hash lines, indicating they are equal in length. - Similarly, the line segments \( CE \) and \( DE \) are also marked with hash lines, suggesting they are equal in length to each other. - **Visual Representation**: - The diagram is a side view, suggesting equal line segments contribute to congruent triangles or particular geometric properties. This image can be used to demonstrate geometric concepts such as intersecting lines, congruent triangles, or other properties like parallel lines and transversal properties.
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