Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Understanding Similar Triangles In this lesson, we will explore the concept of similar triangles using a practical example involving triangular tiles used on the roof and window of a shuttle. #### Example: A diagram of a triangular tile used on the roof of the shuttle is shown below. A similar triangular tile, with a short leg measuring 6 inches, is used near the window. ![Diagram of Triangular Tiles](insert_image_url_here) 1. **Roof Tile:** - Height: 9 inches - Base: 15 inches 2. **Window Tile:** - Height: 6 inches - Base: ? **Note:** Figures are not drawn to scale. Since the two triangles are similar, the ratio of the corresponding sides is equal. To find the length of the longer leg of the window tile, we set up the following proportion based on the height: \[ \frac{\text{Height of Roof Tile}}{\text{Height of Window Tile}} = \frac{\text{Base of Roof Tile}}{\text{Base of Window Tile}} \] Substitute the given values: \[ \frac{9 \text{ inches}}{6 \text{ inches}} = \frac{15 \text{ inches}}{x} \] Cross-multiply and solve for \( x \): \[ 9x = 6 \times 15 \] \[ 9x = 90 \] \[ x = \frac{90}{9} \] \[ x = 10 \] Therefore, the length of the longer leg of the window tile is **10 inches**. ### Question Which is the length of the longer leg of the window tile? - [ ] 12 inches - [ ] 9 inches - [ ] 11 inches - [x] 10 inches This exercise demonstrates how similar triangles can be used to solve problems involving proportional relationships.
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Transcribed Image Text:### Understanding Similar Triangles In this lesson, we will explore the concept of similar triangles using a practical example involving triangular tiles used on the roof and window of a shuttle. #### Example: A diagram of a triangular tile used on the roof of the shuttle is shown below. A similar triangular tile, with a short leg measuring 6 inches, is used near the window. ![Diagram of Triangular Tiles](insert_image_url_here) 1. **Roof Tile:** - Height: 9 inches - Base: 15 inches 2. **Window Tile:** - Height: 6 inches - Base: ? **Note:** Figures are not drawn to scale. Since the two triangles are similar, the ratio of the corresponding sides is equal. To find the length of the longer leg of the window tile, we set up the following proportion based on the height: \[ \frac{\text{Height of Roof Tile}}{\text{Height of Window Tile}} = \frac{\text{Base of Roof Tile}}{\text{Base of Window Tile}} \] Substitute the given values: \[ \frac{9 \text{ inches}}{6 \text{ inches}} = \frac{15 \text{ inches}}{x} \] Cross-multiply and solve for \( x \): \[ 9x = 6 \times 15 \] \[ 9x = 90 \] \[ x = \frac{90}{9} \] \[ x = 10 \] Therefore, the length of the longer leg of the window tile is **10 inches**. ### Question Which is the length of the longer leg of the window tile? - [ ] 12 inches - [ ] 9 inches - [ ] 11 inches - [x] 10 inches This exercise demonstrates how similar triangles can be used to solve problems involving proportional relationships.
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