You get a trapezium. (Check it!) Which are the parallel sides here? Should the non-parallel sides be equal? You can get two more trapeziums using the same set of triangles. Find them out and discuss their shapes. 2. Take four set-squares from your and your friend's instrument boxes. Use different numbers of themto place side- by-side and obtain different trapeziums. If the non-parallel sides of a trapezium are of equal length, we call it an isosceles trapezium. Did you get an isoceles trapezium in any of your investigations given above?

To address your questions about trapeziums (or trapezoids, as they are known in some regions), let's break it down step by step. ### 1. Identifying the Parallel Sides In a trapezium, there are two sides that are parallel. These are typically referred to as the "bases" of the trapezium. The other two sides, which are not parallel, are called the "legs." ### 2. Non-Parallel Sides The non-parallel sides (the legs) do not have to be equal in length. If they are equal, the trapezium is classified as an **isosceles trapezium**. If they are of different lengths, it is simply a trapezium. ### 3. Creating Different Trapeziums Using a set of triangles, you can create different trapeziums by arranging the triangles in various configurations. Here are two possible trapeziums you might create: - **Trapezium A**: Formed by placing two triangles with one base aligned with the other, creating a larger base and a smaller top base. - **Trapezium B**: Formed by arranging triangles in a way that the legs are of different lengths, resulting in a more skewed shape. ### 4. Using Set-Squares When using set-squares, you can create trapeziums by placing them side by side in various orientations. For example: - **Trapezium C**: If you place two set-squares with one side aligned parallel to the other, you can create a trapezium with one base longer than the other. - **Trapezium D**: By using three set-squares, you can create a trapezium with a more pronounced angle on one side, leading to a different shape. ### 5. Isosceles Trapezium In your investigations, if you find that the non-parallel sides (legs) of any trapezium you created are of equal length, then you have indeed created an **isosceles trapezium**. This shape is characterized by its symmetry, where the angles adjacent to each base are equal. ### Conclusion In summary, the parallel sides of a trapezium are its bases, and the non-parallel sides do not need to be equal unless it is an isosceles trapezium. By experimenting with triangles and set-squares, you can create various trapeziums, including isosceles ones, depending on how you arrange the shapes.