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Such a pentagon cannot exist.
Suppose there is a pentagon, ABCDE.
A line of symmetry must pass through a vertex and the midpoint of the opposite side - otherwise there will be more vertices on one side than on the other.
Suppose a line of symmetry passes through A.
Then AB = AE and BC = ED
and ÃB = ÃE and ÃC = ÃD.
Now the second line of symmetry can pass through an adjacent vertex (B or E) or a non-adjacent vertex (C or D). By symmetry, the choice between B and E is irrelevant so suppose the line of symmetry is though B.
Then BA = BC and AE = CD.
and ÃC = ÃA and ÃD = ÃE.
Combining this with the earlier result, all five sides are of equal measure, as are all five angles and so the pentagon is regular and has 5 lines of symmetry.
Alternatively, if the second line of symmetry passes through C, then
CB = CD and BA = EA
and and
ÃB = ÃD and ÃA = ÃE.
So, again, combining this with the first result, all five sides are of equal measure, as are all five angles and so the pentagon is regular and has 5 lines of symmetry.
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∙ 10y ago
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What shapes have more than two lines of symmetry?
A decagon and any polygon above a pentagon has more than two lines of symmetry
Does a pentagon have two lines of symmetry?
No- it has five (one from each corner to the other side) Incorrect. It depends on which type of pentagon your talking about, if you are talking about an equilateral regular pentagon, yes 5 sides but if you are talking about an irregular pentagon, well, that's different. a regular pentagon has 5 lines of symmetry
Does every rectangle have exactly two lines of symmetry?
Yes, unless its a square, then there are four lines of symmetry.
If it has exactly two lines of symmetry it must be a quadrilateral?
Not at all. There are an infinite number of figures that have two lines of symmetry. For a start, an ellipse.
What quadrilateral has exactly 2 lines of symmetry?
There are two quadrilaterals with 2 lines of symmetry. A rhombus and a rectangle (if they are not also a square)
Can you make a pentagon with exactly two lines of symmetry?
No. A pentagon can have 1 or 5 lines of symmetry.
What shapes have more than two lines of symmetry?
A decagon and any polygon above a pentagon has more than two lines of symmetry
What is a quadrilateral that has exactly two lines of symmetry?
A four-sided quadrilateral having two lines of symmetry is a rectangle
Does a rectangle or square have exactly 2 lines of symmetry?
Technically, a square is a rectangle with four lines of symmetry. A non-square rectangle has exactly two lines of symmetry: the vertical and the horizontal.
Does every rectangle have exactly two lines of symmetry?
Yes, unless its a square, then there are four lines of symmetry.
Does a pentagon have two lines of symmetry?
No- it has five (one from each corner to the other side) Incorrect. It depends on which type of pentagon your talking about, if you are talking about an equilateral regular pentagon, yes 5 sides but if you are talking about an irregular pentagon, well, that's different. a regular pentagon has 5 lines of symmetry
If it has exactly two lines of symmetry it must be a quadrilateral?
Not at all. There are an infinite number of figures that have two lines of symmetry. For a start, an ellipse.
Can you show two lines of symmetry on a pentagon?
Yes! You can actually show five lines of symmetry. Each one goes from the vertex to the midpoint of the opposite side.
What is a counterexample of All rectangles have two lines of symmetry?
Since the statement does not say that they have exactly two lines of symmetry, I do not believe that there is a counter example.
What quadrilateral has exactly 2 lines of symmetry?
There are two quadrilaterals with 2 lines of symmetry. A rhombus and a rectangle (if they are not also a square)
What figure has exactly two lines of symmetry?
with corners: rectangles and rhombiwithout corners: ovals (ellipse)The diagonals are the two lines of symmetry of any rhombus that is not a square.
Draw a shape with two lines of symmetry?
A line of symmetry can be thought of as the line where you could cut a shape (or a line or any object) and it would look the exact same on both sides. An example of a shape with exactly two lines of symmetry would be a rectangle. A square also has at least two lines of symmetry, but it actually has four total.
