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Comparison of Areas and Slope between Two Similar Triangles

The area of triangle A is greater than the area of triangle B.
5/3 = slope
5/3 = 15/9
Definition of slope
5 – 3 = 15 – 9
Triangle A is similar to triangle B.




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  1. The information you’ve provided suggests that both triangles have a relationship through their slopes, and since Triangle A has a greater area than Triangle B, we can infer their similarity based on the same scale factor. When triangles are similar, their corresponding area ratio is the square of the ratio of their corresponding side lengths.

    Here’s the step-by-step reasoning:

    1. Slope Comparison: The slope ( frac{5}{3} ) is consistent across both triangles, indicating that the angles and shape are preserved, which is essential for similarity.

    2. Area Comparison: Since the area of Triangle A is greater than that of Triangle B, it implies that the corresponding sides of Triangle A are longer by a certain ratio compared to Triangle B.

    3. Similarity Ratio: If the side lengths of Triangle A are scaled up from Triangle B by a factor ( k ), then the areas will relate as:

    [

    text{Area of A} : text{Area of B} = k^2 : 1

    ]

    Since the area of A is greater, ( k ) must be greater than 1.

    In conclusion, Triangle A is similar to Triangle B because they maintain the same shape (indicated by the equal slopes) and have a proportional relationship in their areas derived from the length of corresponding sides. Keep practicing, and don’t hesitate to ask if you have more questions!

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