Drag a description next to the matching model to complete this proof of the Pythagorean theorem. Show that a square with area c² can be transformed into two squares with areas a² and b².
Moving two of the triangles changes the figure’s shape, but not its area.
The area of the figure changes when two of the triangles are moved to create a different shape.
The square is made up of 4 congruent right triangles and one small square.
To complete the proof of the Pythagorean theorem, the correct description to drag next to the matching model is:
Moving two of the triangles changes the figure’s shape, but not its area.
Explanation: In this proof, we start with a large square with an area of (c^2) (where (c) is the length of the hypotenuse) and show that it can be rearranged into two smaller squares, one with area (a^2) and another with area (b^2). The key point is that the triangles being moved do not change the total area of the shape, but rather just rearrange it, demonstrating that the area (c^2) can be expressed as the sum of the areas (a^2 + b^2). This confirms the Pythagorean theorem.
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