Can anyone tell me what a hexagon with two sides of symmetry and four acute angles look like?

Question

This is a question I have for my Maths home-work. I am aged 10.

Answer 1

I don't think you can have 4 acute angles in a hexagon.

Answer 2

In Geometry as in most Mathematics definition is critical.
A polygon is made of some number of straight line segments connected end to end with two and only two ends at every intersection and no pair of line segments crossing each other. The minimum number of sides possible is 3. That is called a triangle.
A 4 sided polygon is called a quadrilateral. Squares and rectangles are two types of quadrilaterals.
A 5 sided polygon is called a pentagon.
A hexagon is a six sided polygon.
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Angles are described in relationship an angle called a right angle. A right angle is the kind of angle that is the corner of a square.
An obtuse angle is one that is wider than a right angle.
An acute angle is one that is narower than a right angle.
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I will assume that the problem stated two lines of symmetry rather than two sides of symmetry. A line of symmetry is a line that can be drawn that divides a figure into two parts that have the same shape in the same way that your image in a mirror looks the same as you.
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The six internal angles of the hexagon must be in pairs of identical angles for it to be possible to draw a line of symmetry.
Since four of the angles are acute angles, the two remaining angles must be so large that they point toward the inside of the hexagon. The smaller the acute angles the sharper the internally pointing angles will be.
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I believe this is the best I can do with words and no pictures.

Answer 3

Your question is a little difficult for me to understand. Im not sure what "two sides of symmetry" means. It could mean:
two of the 6 sides are the same length and have both of their angles (with adjacent sides) the same
a line drawn thru the center of the hexagon divides the figure into two pieces which can be rotated or reflected or inverted into one another
or there are two of these lines thru the center
My guess is an hourglass figure would do it :
> < connect top ends and bottom ends
left and right side are symmetrical and so are top and bottom.
But I could also draw a triangle with the two sides having equal acute angles like a V and after I connect the top side I could take out a slanting "v" leaving FOUR lines instead of one on the top. One of the angles of the slanting "v" cut out would have to be acute to satisfy the requirements of your problem but note that the angles and lengths of the two sides of the big V are symmetrical (but not the hexagons shape).
I am not sure if other possibilities exist.

Answer 4

Yes, but how can I show you?

I'll try to sketch it:-

*************
....*............*
.......*......*
....*............*
*************

The shape is draw in * (stars). It has six sides, and four acute angles. It has two LINES of symmetry, vertical and horizontal lines through the middle.

Your question said two SIDES of symmetry, I have never heard of "SIDES" of symmetry before, only lines of symmetry. I assume you just wrote the wrong word.