How can a teacher demonstrate that a triangle is equivalent to half a square?

To demonstrate that a triangle is equivalent to half a square, reflecting the triangle along its longest side provides a visual and geometric representation of this relationship. When a right triangle is reflected along its longest side, it creates a second triangle that, when combined with the original triangle, forms a rectangle or a square, thereby visually confirming that the area of the triangle is indeed half that of the square.

This method effectively illustrates the geometric principles of congruence and symmetry while providing an accurate measurement perspective that reinforces the concept of area. The transformation involved in the reflection helps students visualize how the area is divided, solidifying their understanding of the relationship between triangles and squares.