Question

use the diagram to the right to answer questions 5 - 8.

1. how many planes are shown in the figure?
2. give another name for plane w.
3. name the intersection of plane ade and plane w.
4. name a point non - collinear to points a and b.

Explanation:

Step1: Identify planes in the figure

A plane is a flat surface. In the given figure, the base is plane \(W\), and the triangular faces are plane \(ADE\), plane \(ABE\), plane \(BCE\), plane \(CDE\). So there are \(5\) planes in total.

Step2: Another name for plane \(W\)

A plane can be named by three non - collinear points on the plane. Points \(A\), \(B\), \(C\) (and \(D\)) are on plane \(W\). So another name for plane \(W\) is plane \(ABCD\) (or other combinations of three non - collinear points on plane \(W\) like plane \(ABD\) etc.).

Step3: Intersection of plane \(ADE\) and plane \(W\)

The intersection of two planes is a line. Looking at the figure, the intersection of plane \(ADE\) and plane \(W\) is line \(AD\).

Step4: Non - collinear point to \(A\) and \(B\)

Points \(C\), \(D\), \(E\) are non - collinear to \(A\) and \(B\). For example, point \(E\) (or \(C\) or \(D\)).

Answer:

1. \(5\)
2. Plane \(ABCD\) (or other valid names)
3. Line \(AD\)
4. Point \(E\) (or \(C\) or \(D\))