Q: What is the mathematical name for a quadrilatural shape that has 2 long sides the same length 2 short sides the same length and does not have any right angles and does not have reflective symmetry?

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If all the sides and angles of a pentagon were equal, you would be able to put a mirror through the centre, and have the reflection be equal to the original image. This means that it would have reflective symmetry. If a pentagon does not have reflective symmetry, then it's angles and side lengths cannot all be the same. Thus, it is an irregular pentagon.

Any line through a circle has reflective symmetry about the radius that is at right angles to it.

a rectangleImproved Answer:-It is a parallelogram

A circle has an infinite number of angles of rotational symmetry.

Parrallelogram (it has rotational symmetry but no lines of symmetry)

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360o

A trapezoid

If all the sides and angles of a pentagon were equal, you would be able to put a mirror through the centre, and have the reflection be equal to the original image. This means that it would have reflective symmetry. If a pentagon does not have reflective symmetry, then it's angles and side lengths cannot all be the same. Thus, it is an irregular pentagon.

Any line through a circle has reflective symmetry about the radius that is at right angles to it.

a rectangleImproved Answer:-It is a parallelogram

A circle has an infinite number of angles of rotational symmetry.

infinite angles of rotational symmetry... (: ~kitty <3 = =

If your asking what shape has three lines of symmetry, your answer would be an equilateral triangle. You can tell how many lines of symmetry a shape that has all angles of the same measure has by looking at it's angles. Ex., pentagon has five angles--five lines of symmetry; octagon has eight angles, eight lines of symmetry; etc.

Parrallelogram (it has rotational symmetry but no lines of symmetry)

2 axes from angles to angles

Only the pair of angles opposite the line of symmetry are equal. The other two angles that are bisected by the line of symmetry are not equal. if these angles were equal then the shape would be a rhombus.

A rectangle. Obviously the right angles are in the four corners of the rectangle. The lines of symmetry occur across the horizontal and vertical. There are no lines of symmetry on the diagonal.