Sketch and color/shade two distinct coplanar half-planes whose union is a half-plane. Make sure it is clear what is the edge and the two half-planes.
www.geogebra .org/classic
Use this to help you build it, you can change the color of the planes to!
Yeh but I dont understand how I can build it overall, but thx for the link it helped me on another problem. How is it possible for the union of two half-planes to be half-plane?
To sketch and color/shade two distinct coplanar half-planes whose union is also a half-plane, follow these steps:
1. Start by drawing a straight line on a piece of paper, representing the edge of the two half-planes. Label this line as the edge.
2. Now, choose any point on one side of the edge and mark it as a point within the first half-plane.
3. Next, draw a dashed line starting from the selected point and extending beyond the edge, in a direction away from the other side of the edge. This dashed line represents the boundary of the first half-plane.
4. Label the first half-plane clearly and color it in using a solid color or shade it with horizontal or vertical lines.
5. To create the second half-plane, choose any point on the other side of the edge (opposite to the first half-plane's side) and mark it as a point within the second half-plane.
6. Repeat step 3 by drawing a dashed line starting from this newly selected point, also extending beyond the edge but in the opposite direction compared to the first half-plane. This dashed line represents the boundary of the second half-plane.
7. Label the second half-plane distinctly and assign it a different color or shading pattern from the first half-plane.
8. Ensure that the two half-planes are distinct by making sure that the shaded or colored areas do not overlap or touch each other. Each half-plane should be clearly separated by the edge.
Remember, the union of these two distinct half-planes will form a larger half-plane when combined, with the edge serving as the boundary and dividing the entire space.