This picture shows a proof of the Pythagorean theorem because

Question

This picture shows a proof of the Pythagorean theorem because

Two diagrams, labeled Figure 4-A and Figure 4-B, are presented side-by-side.

Both diagrams show a square divided into smaller geometric shapes. Each square is outlined in a light orange/yellow color. In Figure 4-A, the inside of the square is divided into smaller sections that form a larger, central quadrilateral shape that is not fully filled in. The smaller triangles and squares around the central quadrilateral are labelled with single letters(a, b, and c). There is a small label 'c²' contained within the central quadrilateral.

In Figure 4-B, the inside of the larger square is divided into triangles. A few of the triangles are labeled with single letters( a, b and c). The smaller triangles are labeled with exponents such as 'b²' and 'a²'. The labeling of the smaller squares or triangles is visually more distinct.

(1 point)
Responses

The yellow triangles fill up the large squares just enough to have a small square in each figure.
The yellow triangles fill up the large squares just enough to have a small square in each figure.

a < b < c, so the Pythagorean theorem holds true.
a < b < c, so the Pythagorean theorem holds true.

The four yellow triangles are congruent in both large squares and the large squares are congruent, so c2=a2+b2The four yellow triangles are congruent in both large squares and the large squares are congruent, so c squared is equal to A squared plus b squared

a = b = c, so the Pythagorean theorem holds true.

1 answer

Based on the description you've provided about the two diagrams related to the Pythagorean theorem, the most suitable response would be:

The four yellow triangles are congruent in both large squares, and the large squares are congruent, so \(c^2 = a^2 + b^2\).

This statement correctly summarizes the reasoning behind the Pythagorean theorem, which states that in a right triangle, the area of the square on the hypotenuse (c) is equal to the sum of the areas of the squares on the other two sides (a and b). The congruence of the triangles supports the equality.

Ask a New Question or answer this question.

GPT-4o mini · Answer

Based on the description you've provided about the two diagrams related to the Pythagorean theorem, the most suitable response would be:

The four yellow triangles are congruent in both large squares, and the large squares are congruent, so \(c^2 = a^2 + b^2\).

This statement correctly summarizes the reasoning behind the Pythagorean theorem, which states that in a right triangle, the area of the square on the hypotenuse (c) is equal to the sum of the areas of the squares on the other two sides (a and b). The congruence of the triangles supports the equality.