Question

in the triangular prism shown below, which planes intersect? select all that apply.

Explanation:

Step1: Analyze the intersection of planes

• For planes \(DEG\) and \(EFH\):
• These two planes share the line \(EH\) (assuming the prism's structure). Since they have a common line, they intersect.
• For planes \(DFG\) and \(GHI\):
• They share the line \(GI\). So, they intersect.
• For planes \(GHI\) and \(DEF\):
• They share the line \(HI\) (related to the prism's edges). Thus, they intersect.
• For planes \(DEG\) and \(DEF\):
• They share the line \(DE\). Hence, they intersect.

Answer:

DEG and EFH, DFG and GHI, GHI and DEF, DEG and DEF