Proving Parallelograms: ABCDEFGH with IJK

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SUMMARY

The discussion focuses on proving that line EK and line FG are parallel within the context of a cube ABCDEFGH with a side length of 3 cm. The points I and J are defined using vectors, specifically vector BI as 1/5 of vector BF and vector CJ as 4/5 of vector CG. The intersection point K is established by the plane EIJ cutting line HG. The problem requires a geometric proof of parallelism between the specified lines.

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orangeSLICE
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Hello :D

ABCDEFGH is a cube with a side of 3cm. The points I and J are defined by:

vector BI = 1/5 of vector BF
vector CJ = 4/5 of vector CG

The plan (EIJ) cuts line (HG) into K.

1. Prove that line (EK) and line (FG) are parallele.

Any suggestions on how to go about this?
 
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I really don't think the problem you posted is correct. Please re-check the problem.
Viet Dao,
 

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