To solve the problem, we will need to determine the slopes of triangles \( \triangle ABC \) and \( \triangle AGH \). Since I do not have access to the image, I'll explain the general process for finding the slopes of triangles based on coordinates.
Part A: Slope of ΔABC
To find the slope of triangle ΔABC, we first need the coordinates of points A, B, and C. The slope (\( m \)) can be calculated with the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let’s assume the coordinates are:
- \( A(x_1, y_1) \)
- \( B(x_2, y_2) \)
- \( C(x_3, y_3) \)
If A and C are the points along the ramp, use those coordinates:
- \( A \) and \( C \) provide the vertical and horizontal measurements of the triangle.
- Find the slope between points A and C, as they typically represent the endpoints of the ramp.
Assuming you find the coordinates, plug them into the slope formula.
Part B: Slope of ΔAGH
Now, repeat the same process for triangle ΔAGH. Again, you will need the coordinates from points A, G, and H.
- Let’s assume the coordinates are:
- \( A(x_1, y_1) \)
- \( G(x_4, y_4) \)
- \( H(x_5, y_5) \)
Use points A and H (assuming they represent the endpoints of the larger triangle) to find the slope:
\[ m = \frac{y_5 - y_1}{x_5 - x_1} \]
Part C: Comparing the Slopes
Once you have both slopes \( m_{ABC} \) for triangle ΔABC and \( m_{AGH} \) for triangle ΔAGH, you can compare them directly.
- If \( m_{ABC} > m_{AGH} \): Triangle ΔABC is steeper.
- If \( m_{ABC} < m_{AGH} \): Triangle ΔAGH is steeper.
- If \( m_{ABC} = m_{AGH} \): They have the same steepness.
Conclusion
To finalize your answers, determine the specific coordinates from the image and plug them into the slope formula for both triangles. This will give you the slopes and allow you to compare them. If you can provide any numerical coordinates, I can help you calculate the exact slopes!