Question
When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square.
Determine if each set of three squares supports this statement or does not support this statement and drag the set to the appropriate box. Note: Squares are not drawn to scale.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Supports Statement Does NOT Support Statement
Determine if each set of three squares supports this statement or does not support this statement and drag the set to the appropriate box. Note: Squares are not drawn to scale.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Supports Statement Does NOT Support Statement
Answers
Answered by
GPT-4o mini
To determine if each set of squares supports or does not support the statement about the relationship between the areas of the squares when they are joined to form a right triangle, we can use the Pythagorean theorem. According to the theorem, in a right triangle, the sum of the areas of the two smaller squares (whose sides are the lengths of the two legs of the triangle) should equal the area of the largest square (whose side is the length of the hypotenuse).
Here’s how you can categorize the sets based on whether they adhere to this relationship:
1. **Supports Statement**: If the squares' areas conform to the equation \( A_1 + A_2 = A_3 \) (where \( A_1 \) and \( A_2 \) are the areas of the two smaller squares and \( A_3 \) is the area of the largest square), then that set supports the statement.
2. **Does NOT Support Statement**: If the squares do not satisfy the equation and the combined area of the two smaller squares is not equal to the area of the largest square, then that set does not support the statement.
For you to categorize the squares appropriately, check the areas of each set and compare them according to the Pythagorean theorem. Based on that analysis, drag each set into the corresponding box (either "Supports Statement" or "Does NOT Support Statement").
If specific sets were provided, I could help you analyze them directly. Please share them to continue!
Here’s how you can categorize the sets based on whether they adhere to this relationship:
1. **Supports Statement**: If the squares' areas conform to the equation \( A_1 + A_2 = A_3 \) (where \( A_1 \) and \( A_2 \) are the areas of the two smaller squares and \( A_3 \) is the area of the largest square), then that set supports the statement.
2. **Does NOT Support Statement**: If the squares do not satisfy the equation and the combined area of the two smaller squares is not equal to the area of the largest square, then that set does not support the statement.
For you to categorize the squares appropriately, check the areas of each set and compare them according to the Pythagorean theorem. Based on that analysis, drag each set into the corresponding box (either "Supports Statement" or "Does NOT Support Statement").
If specific sets were provided, I could help you analyze them directly. Please share them to continue!