I am trying to identify whether the following objects possess planes of symmetry or not, but my answers seem different, from the textbook solutions (Klein Organic Chemistry 2e, Page 220, Question 23). Some of them I am unsure of and would like to make sure I know the proper reasoning for. Can someone please clarify?

(b) The correct response is yes. Is the plane of symmetry I have drawn acceptable? (c) The correct response is no, but I thought it is possible to have a plane of symmetry like the one I have drawn. (e) The correct response is yes, which I think I understand. I think this has three planes of symmetry. (f) The correct response is no, which I agree with. However, it doesn't seem to concur with the response for the follow-up question.

Follow-up: Which image has three planes of symmetry? The correct answer is apparently, (f). My response would have been (e).

enter image description here

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    $\begingroup$ The follow-up question\answer must be wrong. F has no plane of symmetry while E has 3 planes as you've identified. I think C has a plane (the one you've drawn) too, unless the two metal pieces are not symmetric, it's a little hard to tell from the drawing. $\endgroup$ – ron May 13 '15 at 16:37
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    $\begingroup$ For (e), assuming the holes go all the way through the brick, the third plane of symmetry would be cutting halfway deep through, not diagonally as is drawn. $\endgroup$ – jerepierre May 13 '15 at 16:40
  • $\begingroup$ I couldn't take a picture of the image in my textbook so I tried to find a similar one (mainly in terms of the angle of the picture, because I thought that matters); however, the brick has three holes, all rectangular and evenly spaced. $\endgroup$ – imaginov May 13 '15 at 16:46

Let us address the elephant in the room first and foremost. All of these objects do not have any symmetry if you wanted to get real technical about it. However, let us just assume certain things for this useful exercise to be relevant.

b.) The teacup has a vertical plane of symmetry splitting the teacup in half along the handle axis and intersecting with the centroid of the cup and saucer. I would say that your guess is correct though it would be useful to have drawn in a plane rather than simply a line (for all examples).

c.) At first glance the pliers have a couple planes of symmetry BUT upon further thought it may not due to the way the rotating JOINT is constructed. See the example below:


While it is difficult to see in your picture, below it is made very clear. Therefore I will say that this object does not contain a plane of symmetry. It would be POSSIBLE that it could have a plane of symmetry, one that lies in the plane of your monitor screen, cutting the object in half from tip to handle end... but it would be impossible to tell without seeing the other side. Many times pliers come with an inscription on one side of the joint, thereby breaking this symmetry.

e.) The brick does indeed have multiple planes of symmetry. One vertical plane bisects the brick along its width and one bisects the brick along its length. In addition, one plane of symmetry lies in the plane of the brick (the plane the brick is lying on), cutting the brick in half (think of it as coming in through the side of the brick).

f.) The hand has no plane of symmetry that I can see at all. The back of the hand doesn't look like its front... the left and right side of the hand are clearly not mirror images of each other...

The brick has three planes of symmetry.

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  • $\begingroup$ I never thought about the inscription aspect of the pliers. Thank you for your insightful response! $\endgroup$ – imaginov May 19 '15 at 15:44

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