Question

The figure shown is a rectangular prism. Which edges are parallel to HK ?

Select each correct answer.
__
PB
__
AM
__
YD
__
HA
__
BM

Answer 1

PB, AM, YD

Explanation:

Hello there! a rectangular prism has exactly 12 edges. Its shape determines 3 groups of 4 edges each parallel between them. In this case, these groups of edges are:

PB, AM, YD, HK

AH, MK, BD, PY

PA, BM, YH, DK

Answer 2

Line HK is the line of intersection between pllanes AMKH and HKDY.

Consider all given options:

1. Line PB is the line of intersection between pllanes APBM and PBDY. Since planes APBM || HKDY and AMKH || PBDY, then lines PB and HK are parallel.

2. Line AM is the line of intersection between pllanes APBM and AMKH. Since planes APBM || HKDY and parallel planes are cut by plane AMKH, then lines AM and HK are parallel.

3. Line YD is the line of intersection between pllanes HKDY and AMKH. Since planes AMKH || PBDY and parallel planes are cut by plane HKDY, then lines YD and HK are parallel.

4. Lines HA and HK intersect each other at point H, thus they are not parallel.

5. Lines BM and HK are not parallel, because MB || DK and DK intersect HK at point K.

Answer: correct choices are A, B, C.