PAT Keyhole Question - How to determine if two things have the same height?

[Empathetic Dreamer]

I was wondering if anybody knows a systematic way to determine whether two lines have the same length. Would the way you approach this change depending on the angle of the object as well?

As one example, how might I systematically determine if the length of the two platforms are the same height in the picture I attached? Same goes for the edged structure in the middle.

Thank for the help!

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[spdental]

Draw a mental line from the top of the platform on the left to the top of the platform on the right. If these lines connect, then this is the same height. If they do not (figure in the middle) they will be much lower. See attached.

 

[Empathetic Dreamer]

But couldn't I theoretically draw a line connecting any two points? How would this prove that they are the same height? Is the catch that there needs to be a common reference point?

 

[spdental]

Not where both straight lines of the of the platforms meet perfectly, that would be impossible unless it was the same height.