Question: why cant an equal sided rhombus have 3 lines of symmetry? you have one line of the contrary on every of the diagonals, and also there need to be one vertically on an angle. Have the right to you please describe the rule of symmetry come me? say thanks to you!

Tonia

There are two components to this answer.

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You room right about the 2 diagonals being lines of symmetry. Moreover, these 2 lines accomplish at 90 degrees, so with each other they do a half-turn.

If you begin with just that the opposite - something you would acquire by urgently a piece of record to make one line, then folding the edge ago onto itself, do the second perpendicular line, a solitary cut near the shared edge will cut four class of record and cut off a rhombus.

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So those two symmetries space enough, and also a general reduced or general rhombus will not have actually any more mirrors.

HOWEVER, there are SOME special cases where girlfriend do have actually a third (and fourth) line. This will certainly make a square - which is a special form of rhombus. Not only are all the political parties equal, but all the angles room equal as well. Because that these distinct cases, the 3rd line meets the first two, that the diagonals, in ~ 45 degrees, and also is a mirror separating opposite sides.

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So there space two various questions you could be answering:

Is there a rhombus with just two present of symmtry? The answer is yes, if you take it something prefer a lengthy thing "diamond" shape, native a reduced in the urgently above. Is there a different rhombus which does have an ext that two lines the symmtery? The price is yes too - the square go that.

You can play with examples (a program favor Geometer"s Sketchpad is good for such play) and see that IF there space three lines for any type of figure v only four vertices, a,b,c,d, climate there will be 4 lines and the number will it is in a square.

This is feasible to observe, however not easy to prove except by looking very closely at the possible places peak a can go under such a symmetry. Friend will find that if a can go to two other vertices, then it have the right to go to all three other vertices. This will display the 4 angles space the same too - so friend do have a square.