Question 8

Paper folding helps us understand geometric shapes and their properties through creases.

Step 1 — Understanding the initial folds

We start with a sheet of paper. First, we fold it in half. Then, we fold it once more. This makes the paper a quarter of its original size. When unfolded, this creates four equal sections.

Step 2 — Identifying the shape from creases (Question 4)

We make a triangular crease at one corner. This corner is the middle of the original paper. The image shows the two sides of the triangular flap are equal. When we open the sheet, the creases form a diamond shape. This diamond shape is called a rhombus.

$\boxed{\text{Rhombus}}$

Step 3 — Replicating nested creases (Question 5)

The image for this question shows many nested diamond shapes. To get the first diamond, we fold the corner as in step 3. To get the next smaller diamond, we repeat this action. We fold the new, smaller corner created by the previous fold. We repeat this process multiple times.

Step 4 — Forming a square (Question 6)

The shape formed by the creases in step 4 is a rhombus. A square is a special type of rhombus. For the creases to form a square, the rhombus must have 90-degree angles. This happens if the quarter paper itself is a square. So, if the original paper is a square, the quarter paper is also a square. Then, folding its corner as in step 3 will form a square.

Answer

(i) The shape formed by the creases is a rhombus. (ii) We would repeatedly make triangular creases at the innermost corner of the folded paper. (iii) We would fold the quarter paper's corner as shown in step 3, ensuring the original paper was a square.