All triangles with the same base and height have the same area. Therefore, if we place a base of the triangles on a geoboard, choose a third point at a distance from this base, and draw a line parallel to this base, we can then choose any point on this parallel line to form a triangle. We can thus create an infinite number of triangles with the same area.
This is because all these triangles will have the same base and height. The base is the line segment on the geoboard that we used to create the parallel line, and the height is the distance between this line and the third point we chose.
Given that the parallel line is always at the same distance from the base, the height of the triangle will always be the same. This means that all the triangles we create will have the same area, as they all have the same base and height.
Moreover, by choosing any point on the parallel line, we can vary the shape of the triangle while maintaining the same area. This is possible because the parallel line allows us to modify the length of one side of the triangle while keeping the other two sides fixed (as they are the base and height).
Overall, this demonstrates the important principle that the area of a triangle is determined by its base and height, not by the shape or orientation of the triangle.
