Number 9. Mary had a piece of paper. She folded it exactly in half, then she folded it exactly in half again. She got this shape, and here we have what looks like an isosceles right triangle. Which of the shapes, P, Q, or R, could have been the shape of her original piece of paper? Okay, so as we mentioned, Mary has formed an isosceles right triangle. So right triangles, when we think about it, can be formed by having in two ways. So one way, we can take a square, we can fold it on its diagonal, and that will give us one. Or two, we can take a larger right triangle and fold it along this axis of symmetry right here. And that will give us another right triangle, now with the right angle over here. And these two sides equal in length, here and here. So shape P can be folded vertically across this line to make a square, and then diagonally to a right triangle. Shape Q can be folded diagonally to a right triangle, then again on that right triangle's axis of symmetry. And shape R can be folded on this axis of symmetry once, and then on this axis of symmetry of the new triangle once. Because of that, the answer is E, any of P, Q, or R.

paper folding

isosceles right triangle

original shape

symmetry

folding problem