Question
Which pair of triangles can be used to show that the slope of line a is the same anywhere along the line?
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mediaENV68_FL_8_02_06_OLQ_D1545311658.jpg
mediaENV68_FL_8_02_06_OLQ_A1545311654.jpg
mediaENV68_FL_8_02_06_OLQ_B1545311656.jpg
mediaENV68_FL_8_02_06_OLQ_C1545311655.jpg
mediaENV68_FL_8_02_06_OLQ_D1545311658.jpg
Answers
GPT-4o mini
To determine which pair of triangles can be used to show that the slope of line \( a \) is the same anywhere along the line, we need to consider triangles that are formed by selecting two distinct points along the line and drawing horizontal and vertical lines to create right triangles.
The key is to look for pairs of triangles that share a common angle at one endpoint, and have sides that are parallel to the original line, ensuring that the rise/run ratio remains constant.
Without the visual provided, here are the steps you can follow to identify the correct pair:
1. **Identify Triangles:** Look for triangles that both lie against the same line (line \( a \)).
2. **Common Angle:** Check if these triangles can be shown to have a common angle, indicating that they are similar by AA (Angle-Angle) similarity.
3. **Compare Ratios:** Ensure that the rise (vertical distance) and run (horizontal distance) remain proportional, consistent with the definition of slope.
Once you find the triangle pairs that satisfy these conditions, those will demonstrate that the slope of line \( a \) does not change regardless of the points selected.
If you can provide a more detailed description of the triangles or their properties, I can help further.
The key is to look for pairs of triangles that share a common angle at one endpoint, and have sides that are parallel to the original line, ensuring that the rise/run ratio remains constant.
Without the visual provided, here are the steps you can follow to identify the correct pair:
1. **Identify Triangles:** Look for triangles that both lie against the same line (line \( a \)).
2. **Common Angle:** Check if these triangles can be shown to have a common angle, indicating that they are similar by AA (Angle-Angle) similarity.
3. **Compare Ratios:** Ensure that the rise (vertical distance) and run (horizontal distance) remain proportional, consistent with the definition of slope.
Once you find the triangle pairs that satisfy these conditions, those will demonstrate that the slope of line \( a \) does not change regardless of the points selected.
If you can provide a more detailed description of the triangles or their properties, I can help further.