We are given the following diagram and asked which of the statements are not true.
Let's take a look at each of the statements in order to determine which one is not true.
Statement A
We will start by highlighting planes AGE and GED. Each side of the figure represents a plane.
Notice that point H lies on the intersection of the two planes. This means that it lies in both planes. This statement is true.
Statement B
Let's highlight point E and where the planes intersect.
Point E is located at the corner of each of the planes. This means that it is at the intersection of the planes, or the vertex. Therefore, this statement is true.
Statement C
Let's highlight the given plane and points to see if they are on the same plane.
At first glance we see that the points lie on two different sides, and therefore are not on the same plane. However, remember that it takes three points to create a plane.
Although the points do not lie on a plane in the diagram, there exists a plane where they all lie. Therefore, this statement is true.
Statement D
Let's highlight the three points. We will also draw a line through A and H. If this line intercepts point D, the points are collinear.
Since we cannot draw a straight line through the three points, they are not collinear. This statement is not true.
