Question

to build the roof for a paper house, a rectangular paper is cut to form a trapezoid. which diagram shows the correct cuts?

Explanation:

A trapezoid has exactly one pair of parallel sides. A rectangle has two pairs of parallel sides (lengths and widths). To form a trapezoid from a rectangle, we need to make cuts such that after cutting, the resulting figure has one pair of parallel sides (the remaining length - like sides from the rectangle) and the other two sides non - parallel.

• The first diagram: After cutting (the two diagonal - like cuts from the bottom corners to a top point), the resulting figure is a triangle on top of a quadrilateral? No, actually, the remaining figure would not be a trapezoid. The two non - parallel sides here would not form the correct trapezoid structure.
• The second diagram: The cuts are made such that we remove two triangles from the left and right, but the top and bottom sides (which were originally the length sides of the rectangle) remain parallel, and the other two sides (the non - cut sides of the trapezoid) are non - parallel. This fits the definition of a trapezoid (one pair of parallel sides).
• The third diagram: The two diagonal cuts (not from corners) would result in a figure where the sides are not in a trapezoid - like structure. The parallelism is disrupted in a way that doesn't form a trapezoid.
• The fourth diagram: The cuts are from non - corner points on the left and right, and the resulting figure does not have the correct parallel side structure for a trapezoid.

Answer:

The second diagram (the one with the two slanted cuts from the left and right sides, removing small triangles and leaving a trapezoid - shaped figure with the top and bottom sides parallel)