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A square has exactly four lines of symmetry.

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โˆ™ 2014-12-12 15:35:03
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Q: Which figure has exactly four lines of symmetry?
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How many lines of symmetry does x have?

If you mean the letter x, it has four lines of symmetry.

Does a square or rectangle has more lines of symmetry?

They both have the same amount of lines of symmetry. * * * * * Not true. A square has four lines of symmetry, a rectangle only two.

Does a rectangle have four lines of symmetry?

Only two - parallel to and halfway between the sides. The diagonals are not lines of symmetry.

Is it possible for a quadrilateral to have three lines of symmetry?

It can't have exactly three (it can be a square and have four). Reflecting about a line of symmetry swaps at least two corners of the quadrilateral: a corner has to be symmetric to a corner, and if all four were symmetric to themselves, they'd all have to be on a line, which is impossible. Moreover, different lines of symmetry swap different pairs of corners. Once you pick two corners, there is only one line of symmetry which could possibly swap them - the perpendicular bisector of a segment drawn between the two corners. If two different corners are symmetric, that means that their angles are equal. So three lines of symmetry means that there are three pairs of corners with equal angles. Since there are only four corners total, the only way for this to happen is for all four corners to have equal angles. Then it's either a rectangle (which doesn't work - only two lines of symmetry) or a square (which has four lines of symmetry). Neither possibility has exactly three.

Can a quadrilateral with four equal sides have less than four lines of symmetry?


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