Question

in the triangular prism shown below, which planes intersect? select all that apply. hjk and klm hik and hjk hik and hij klm and hij

Explanation:

Step1: Understand the property of intersecting planes

Two planes intersect if they are not parallel and share a common line.

Step2: Analyze each pair

• For \(HJK\) and \(KLM\):

These two planes are not parallel. They share the line \(MK\) (since \(M\) and \(K\) are common points).

• For \(HIK\) and \(HJK\):

These two planes are not parallel. They share the line \(HK\) (since \(H\) and \(K\) are common points).

• For \(HIK\) and \(HIJ\):

These two planes are not parallel. They share the line \(HI\) (since \(H\) and \(I\) are common points).

• For \(KLM\) and \(HIJ\):

These two planes are not parallel. They share the line \(MI\) (by visual inspection of the prism structure).

Answer:

\(HJK\) and \(KLM\), \(HIK\) and \(HJK\), \(HIK\) and \(HIJ\), \(KLM\) and \(HIJ\)