Chapter 1.2, Problem 14WE

To determine

To find: if there are planes that do not intersect out of the five planes that contain the sides of the given pyramid

Answer to Problem 14WE

No

Explanation of Solution

Given:

The diagram:

From the above figure, it can be observed that the planes $RVS,SVT,TVW,WVR$ all intersect at the point V .

And, plane $RVS$ intersects with the plane $RSTW$ on the line $\overleftrightarrow{RS}$ .

Similarly, plane $SVT$ intersects with the plane $RSTW$ on the line $\overleftrightarrow{ST}$ .

Similarly, plane $TVW$ intersects with the plane $RSTW$ on the line $\overleftrightarrow{TW}$ .

Similarly, plane $WVR$ intersects with the plane $RSTW$ on the line $\overleftrightarrow{WR}$ .

Thus, all the planes intersect each other.