[MOVED] lines of symmetry: how many for a rectangle?

[Chris's Mom]

I'm having a problem with understanding a question my daughter had on a 3rd grade test:

On a rectangle, how many lines of symmetry are there?

Her teacher says there are two. I say there are 4: vertical, horizontal, and 1 each corner to corner. If you cut each line every triangle matches.

My dictionary defines symmetry as "due portion between several parts of an object; exact corespondence of opposite sides of an object."

Her teacher says only if you can fold the paper corner to corner and they match is the shape symmetrical.

Any help would be appreciated!!

 

[stapel]

You might want to ask the teacher how "symmetry" is defined.

I've never heard of a mathematical definition that would accept the diagonal of a rectangle as being a line of symmetry: If you rotate the rectangle about that diagonal, yes, you would still have a rectangle, but not the same one. The new rectangle would be rotated away from the original one.

B-------C                     ,C
|       |                  /    \   
|    /  |               /   /    \
|       |            /            \ 
|   /   |          D       /       B
|       |           \            /
|  /    |            \    /   /
|       |             \    /  
A-------D -> rotate -> A'

In the above, holding at A and twirling about the line AC (so B arcs over the rectangle, moving over to the right) leaves A unmoved. But the move flips side AD under and around to the left. The diagonal doesn't move, so the sides must. This leaves you in a different position.

Since the move is "noticable" (that is, since you can see a change), this line is not an axis of symmetry, at least not according to the usual definitions.

If her teacher is using some non-standard definition which would lead to an answer of "4", she should provide this definition.

Eliz.

 

[skeeter]

I'm having a problem with understanding a question my daughter had on a 3rd grade test:

On a rectangle, how many lines of symmetry are there?

Her teacher says there are two. I say there are 4: vertical, horizontal, and 1 each corner to corner. If you cut each line every triangle matches.

My dictionary defines symmetry as "due portion between several parts of an object; exact corespondence of opposite sides of an object."

Her teacher says only if you can fold the paper corner to corner and they match is the shape symmetrical.

the teacher is correct ... if one part folds on top of the other exactly, i.e. one part is the "mirror" image of the other part, then you have a line of symmetry. folding a square from corner to corner will yield a line of symmetry, but not so for a rectangle that has unequal adjacent sides. the two lines of symmetry for a rectangle are parallel to the pairs of opposite sides and pass through the rectangle's center, as shown below ...

 

[pka]

On a rectangle, how many lines of symmetry are there?
Her teacher says there are two. I say there are 4: vertical, horizontal, and 1 each corner to corner.

And you would have been correct if it had been a square and not a rectangle.

 

[Chris's Mom]

Thanks to all for your help. I now understand. sorry it took so long to reply. I sent it to the wrong folder.