解释下这道新加坡数学题目---**Textual Information:** **Question Stem:** Q3. Which shapes are divided into fourths? **Options:** ☐ A ☐ B ☐ C ☐ D **Chart/Diagram Description:** Type: Geometric shapes with internal divisions. Main Elements: Four shapes are presented horizontally, labeled A, B, C, and D below each shape. Shape A: A circle divided into four vertical segments by three internal vertical lines. The segments appear unequal in width. Shape B: A square divided into four triangular sections by two diagonal lines connecting opposite vertices. The sections appear equal in size. Shape C: A rectangle divided into three sections by two internal lines. The left section is a triangle formed by the left vertical edge and a diagonal line from the top-left corner to the bottom midpoint. The middle section is a rectangle. The right section is a triangle formed by the right vertical edge and a diagonal line from the top-right corner to the bottom midpoint. There are three sections, not four. The sections appear unequal in size. Shape D: A rectangle divided into four smaller rectangular sections by one horizontal line and one vertical line crossing in the center. The four sections appear equal in size.

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In this Singapore math problem, we need to identify which shapes are divided into fourths. 'Fourths' means a shape is divided into four equal parts. Let's examine each shape. Shape A is a circle divided by three vertical lines, creating four sections. However, these sections are not equal in size. Shape B is a square divided by two diagonal lines, creating four triangular sections that are equal in size. Shape C is a rectangle divided into only three sections, not four. Shape D is a rectangle divided by intersecting lines into four equal rectangular sections. Let's analyze Shape A in detail. This is a circle divided by three vertical lines, creating four sections. Looking closely, we can see that these sections have different widths. The first section on the left is narrower than the second section. The third and fourth sections also have different widths. For a shape to be properly divided into fourths, all four parts must be equal in size. Since the sections in Shape A are clearly unequal, this shape is NOT divided into fourths. Remember, 'fourths' requires both the correct number of parts (four) AND equal sizes. Now let's examine Shape B. This is a square divided by two diagonal lines that connect the opposite corners. These diagonals create four triangular sections. When we divide a square with its diagonals, all four resulting triangles are congruent, meaning they have exactly the same size and shape. Each triangle represents exactly one-fourth of the square's area. Since we have four equal parts, Shape B is correctly divided into fourths. This is a perfect example of what we're looking for in this problem - a shape divided into four equal parts. Let's analyze the remaining shapes. Shape C is a rectangle with two diagonal lines that create three sections - a triangle on the left, a quadrilateral in the middle, and a triangle on the right. Since this shape is divided into only three parts, not four, it cannot be divided into fourths. Shape D is a rectangle divided by one horizontal line and one vertical line that intersect in the center. These lines create four smaller rectangles of equal size. Each rectangle is exactly one-fourth of the original shape. Therefore, Shape D is correctly divided into fourths. So far, we've determined that Shapes B and D are divided into fourths, while Shapes A and C are not. Let's summarize our findings. For a shape to be divided into fourths, it must satisfy two conditions: first, it must be divided into exactly four parts, and second, all those parts must be equal in size. Shape A is a circle divided into four sections, but these sections are not equal in size, so it's not divided into fourths. Shape B is a square divided by diagonals into four equal triangular sections, so it is correctly divided into fourths. Shape C is a rectangle divided into only three sections, not four, so it cannot be divided into fourths. Shape D is a rectangle divided by intersecting lines into four equal rectangular sections, so it is correctly divided into fourths. Therefore, the answer to the question 'Which shapes are divided into fourths?' is B and D.