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What is an irregular hexagon?
A regular hexagon is a polygon with six sides where all six angles have the same measurement. (And all six sides have the same length.) If the angles of a hexagon do not all have the same measurement, or if the sides are not all of the same length, then the hexagon is irregular.
Does all sides of a hexagon have to be equal?
They can be but they don't have to be. If they are then it's called a "regular" hexagon.
Is it possible for a hexagon to have all 6 angles equal and not be a regular hexagon?
yes because all of the sides are equal
Does a hexagon have six equal sides or just six sides?
In a "regular hexagon" all sides are equal. For an irregular hexagon there are six sides but they aren't all the same length.
How can you show that all sides and angles of a hexagon are congruent without using a ruler or a protractor?
You can do that by simply proving that the hexagon is a regular hexagon. You could do this by dividing the hexagon into 6 equilateral triangles of the same size successfully that tesselate to form a hexagon, thus proving that all sides are equal.
