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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.
What else can I help you with?
What pentagon has only 2 lines of symmetry?
A regular pentagon has five lines of symmetry, but a specific type of pentagon known as an irregular pentagon can have only two lines of symmetry. An example would be a pentagon where two sides are equal in length, and the angles opposite these sides are equal, creating reflectional symmetry across those two lines. However, the specific arrangement would affect the overall symmetry, so not all irregular pentagons will have exactly two lines of symmetry.
How many symmetry lines are in a pentagon?
A regular pentagon has five lines of symmetry. Each line of symmetry passes through one vertex and the midpoint of the opposite side. This means that the pentagon can be divided into two mirror-image halves along each of these lines. In contrast, an irregular pentagon may have fewer or no lines of symmetry, depending on its specific shape.
What shapes have more than two lines of symmetry?
A decagon and any polygon above a pentagon has more than two lines of symmetry
How many lines of symmetry are in the regular pentagon?
A regular pentagon has 5 lines of symmetry. Each line of symmetry passes through one vertex and the midpoint of the opposite side. This means that the pentagon can be folded along each line such that the two halves match perfectly.
Does every rectangle have exactly two lines of symmetry?
Yes, unless its a square, then there are four lines of symmetry.
Can you make a pentagon with exactly two lines of symmetry?
No. A pentagon can have 1 or 5 lines of symmetry.
What pentagon has only 2 lines of symmetry?
A regular pentagon has five lines of symmetry, but a specific type of pentagon known as an irregular pentagon can have only two lines of symmetry. An example would be a pentagon where two sides are equal in length, and the angles opposite these sides are equal, creating reflectional symmetry across those two lines. However, the specific arrangement would affect the overall symmetry, so not all irregular pentagons will have exactly two 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
How many lines of symmetry are in the regular pentagon?
A regular pentagon has 5 lines of symmetry. Each line of symmetry passes through one vertex and the midpoint of the opposite side. This means that the pentagon can be folded along each line such that the two halves match perfectly.
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.
How many lines of symmetry does an irregular pentagon have?
One or none.
