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10. Shade exactly two of the nine smaller squares so th a. Only one vertical and one horizontal line of symm b. Only two lines of symmetry about the diagonals. c. Only one horizontal line of symmetry. d. Only one line of symmetry about a diagonal. e. No line of symmetry.

10. Shade exactly two of the nine smaller squares so th a. Only one vertical and one horizontal line of symm b. Only two lines of symmetry about the diagonals. c. Only one horizontal line of symmetry. d. Only one line of symmetry about a diagonal. e. No line of symmetry.

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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### Symmetry in a 3x3 Grid of Squares **Problem Statement:** Shade exactly two of the nine smaller squares so that the resulting figure has: a. Only one vertical and one horizontal line of symmetry. b. Only two lines of symmetry about the diagonals. c. Only one horizontal line of symmetry. d. Only one line of symmetry about a diagonal. e. No line of symmetry. **Diagram:** A 3x3 grid is provided, consisting of 9 smaller squares arranged in three rows and three columns. **Explanation:** In this exercise, you are required to shade exactly two of the nine smaller squares within the 3x3 grid. The objective is to achieve the specified type and number of lines of symmetry. Consider the characteristics of each type of symmetry: 1. **Vertical Line of Symmetry:** - A line that splits an image into two mirror-image halves vertically down the middle. 2. **Horizontal Line of Symmetry:** - A line that splits an image into two mirror-image halves horizontally across the middle. 3. **Diagonal Line of Symmetry:** - A line that splits an image into two mirror-image halves diagonally. Depending on which two squares are shaded, the grid can exhibit these lines of symmetry in different configurations: - **Example for option a:** The scenario in which only one vertical and one horizontal line of symmetry are achieved by carefully choosing and shading two squares. - **Example for option b:** Shading two squares that result in symmetry along the diagonals but not vertical or horizontal. - **Example for option c:** Only achieving one horizontal line of symmetry. - **Example for option d:** Shading two squares such that there is symmetry along only one diagonal. - **Example for option e:** Shading squares in a way that results in no lines of symmetry. ### Task: Experiment by shading different pairs of squares in the grid to discover which pairs meet the criteria for each symmetry option listed above.
Transcribed Image Text:### Symmetry in a 3x3 Grid of Squares **Problem Statement:** Shade exactly two of the nine smaller squares so that the resulting figure has: a. Only one vertical and one horizontal line of symmetry. b. Only two lines of symmetry about the diagonals. c. Only one horizontal line of symmetry. d. Only one line of symmetry about a diagonal. e. No line of symmetry. **Diagram:** A 3x3 grid is provided, consisting of 9 smaller squares arranged in three rows and three columns. **Explanation:** In this exercise, you are required to shade exactly two of the nine smaller squares within the 3x3 grid. The objective is to achieve the specified type and number of lines of symmetry. Consider the characteristics of each type of symmetry: 1. **Vertical Line of Symmetry:** - A line that splits an image into two mirror-image halves vertically down the middle. 2. **Horizontal Line of Symmetry:** - A line that splits an image into two mirror-image halves horizontally across the middle. 3. **Diagonal Line of Symmetry:** - A line that splits an image into two mirror-image halves diagonally. Depending on which two squares are shaded, the grid can exhibit these lines of symmetry in different configurations: - **Example for option a:** The scenario in which only one vertical and one horizontal line of symmetry are achieved by carefully choosing and shading two squares. - **Example for option b:** Shading two squares that result in symmetry along the diagonals but not vertical or horizontal. - **Example for option c:** Only achieving one horizontal line of symmetry. - **Example for option d:** Shading two squares such that there is symmetry along only one diagonal. - **Example for option e:** Shading squares in a way that results in no lines of symmetry. ### Task: Experiment by shading different pairs of squares in the grid to discover which pairs meet the criteria for each symmetry option listed above.
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