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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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Two triangles are given. Which statement accurately describes the relationship between the two triangles? 

The image presents a multiple-choice question related to triangle similarity and congruence. The options are as follows: 1. A circle indicating a choice, followed by "△UVW ~ △XZY" 2. A circle indicating a choice, followed by "△UVW ≅ △XZY" 3. A circle indicating a choice, followed by "△UVW ~ △XYZ" 4. A circle indicating a choice, followed by "△UVW ≅ △XYZ" Each option involves two triangles (△UVW and △XZY/△XYZ) with the symbols "~" representing similarity and "≅" representing congruence. The task is to choose the correct relationship between the triangles.
Transcribed Image Text:The image presents a multiple-choice question related to triangle similarity and congruence. The options are as follows: 1. A circle indicating a choice, followed by "△UVW ~ △XZY" 2. A circle indicating a choice, followed by "△UVW ≅ △XZY" 3. A circle indicating a choice, followed by "△UVW ~ △XYZ" 4. A circle indicating a choice, followed by "△UVW ≅ △XYZ" Each option involves two triangles (△UVW and △XZY/△XYZ) with the symbols "~" representing similarity and "≅" representing congruence. The task is to choose the correct relationship between the triangles.
The image displays two triangles labeled as \( \triangle UWV \) and \( \triangle XYZ \). ### Details of Each Triangle: 1. **Triangle UWV**: - **Sides**: - \( UW \) and \( WV \) have a single tick mark, indicating they are of equal length. - \( UV \) has a different length, indicated by a unique tick mark. - **Angles**: - The angle at vertex \( U \) is marked with a single arc. - The angle at vertex \( V \) also has a single arc, indicating it is equal to the angle at \( U \). - The angle at vertex \( W \) is not marked, implying it differs from the angles at \( U \) and \( V \). 2. **Triangle XYZ**: - **Sides**: - \( XZ \) and \( ZY \) have a single tick mark, indicating they are of equal length. - \( XY \) has a different length, denoted by a unique tick mark. - **Angles**: - The angle at vertex \( X \) is marked with a single arc. - The angle at vertex \( Y \) also has a single arc, indicating it is equal to the angle at \( X \). - The angle at vertex \( Z \) is not marked, implying it differs from the angles at \( X \) and \( Y \). ### Geometric Observations: - Both triangles are isosceles triangles, demonstrated by the pairs of equal sides and angles. - The congruent angles in each triangle suggest similarity in their shape, although they may differ in size. - This image is useful for illustrating properties of isosceles triangles in geometry.
Transcribed Image Text:The image displays two triangles labeled as \( \triangle UWV \) and \( \triangle XYZ \). ### Details of Each Triangle: 1. **Triangle UWV**: - **Sides**: - \( UW \) and \( WV \) have a single tick mark, indicating they are of equal length. - \( UV \) has a different length, indicated by a unique tick mark. - **Angles**: - The angle at vertex \( U \) is marked with a single arc. - The angle at vertex \( V \) also has a single arc, indicating it is equal to the angle at \( U \). - The angle at vertex \( W \) is not marked, implying it differs from the angles at \( U \) and \( V \). 2. **Triangle XYZ**: - **Sides**: - \( XZ \) and \( ZY \) have a single tick mark, indicating they are of equal length. - \( XY \) has a different length, denoted by a unique tick mark. - **Angles**: - The angle at vertex \( X \) is marked with a single arc. - The angle at vertex \( Y \) also has a single arc, indicating it is equal to the angle at \( X \). - The angle at vertex \( Z \) is not marked, implying it differs from the angles at \( X \) and \( Y \). ### Geometric Observations: - Both triangles are isosceles triangles, demonstrated by the pairs of equal sides and angles. - The congruent angles in each triangle suggest similarity in their shape, although they may differ in size. - This image is useful for illustrating properties of isosceles triangles in geometry.
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