Select the figures which, when fitted with each other, will form a complete square.
Correct Answer :
Solution :
The correct answer is the option representing Figures 1, 3, and 4 (corresponding to the combination of image_0.webp, image_2.webp, and image_3.webp).
To understand why these three figures fit together to form a complete square, we can analyze the geometric characteristics of each piece:
1. Figure 1 (image_0.webp): This figure is a wedge-like pentagon. It features a vertical flat left boundary, short flat top and bottom sections, and a prominent triangular protrusion pointing to the right.
2. Figure 2 (image_1.webp): This figure is a rectangular block with a large triangular cutout at the bottom edge. It does not fit with the other components to form a closed square of matching dimensions.
3. Figure 3 (image_2.webp): This figure is a right-angled trapezoid. It features a vertical left edge, flat horizontal top and bottom boundaries, and a slanted right edge sloping downwards and outwards.
4. Figure 4 (image_3.webp): This figure has a slanted upper-left edge, a vertical right edge, and a flat horizontal bottom base extending to the right.
Assembly Steps:
- First, place Figure 3 and Figure 4 side-by-side. The slanted right edge of Figure 3 matches the angle of the slanted left edge of Figure 4. Aligning these two complementary slanted boundaries merges them into a single larger geometric block.
- Once Figure 3 and Figure 4 are joined, they form the outer vertical left, vertical right, and horizontal bottom boundaries of the square. However, an open triangular notch remains at the top-middle junction where the pieces meet.
- Finally, take Figure 1, rotate it, and insert its triangular protrusion directly into the remaining notch. The wedge profile of Figure 1 perfectly fills the empty space and aligns its flat left edge (now rotated to the top) to complete the square's top boundary.
Thus, fitting Figures 1, 3, and 4 together completes all four straight outer edges and 90-degree corners of a perfect square without any gaps or overlaps.
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