No, not all axisymmetric triangles are isosceles. An axisymmetric triangle is a triangle that can be rotated 180 degrees and still look the same. Isosceles triangles are a specific type of triangle where two sides are equal in length. While an isosceles triangle can be axisymmetric, not all axisymmetric triangles are isosceles. **

A parallelogram is not axisymmetric because it does not have rotational symmetry around any axis. In an axisymmetric shape, any rotation around a central axis will result in the same shape. However, in a parallelogram, rotating it around any axis other than its center will result in a different orientation and shape. This lack of rotational symmetry around any axis is what distinguishes a parallelogram from an axisymmetric shape. **

The object is axisymmetric because it has rotational symmetry around an axis, meaning it looks the same when rotated around that axis. Point-symmetry, on the other hand, involves reflection symmetry around a point, which is not present in this case. **

No, regularly constructed figures are not always axisymmetric. While axisymmetric figures have rotational symmetry around an axis, regularly constructed figures have equal sides and angles. Some regularly constructed figures, such as squares and equilateral triangles, may also be axisymmetric due to their symmetry properties, but others, like regular pentagons or hexagons, do not possess axisymmetry. **

No, a figure cannot be both axisymmetric and point-symmetric at the same time. Axisymmetric means that the figure has rotational symmetry around an axis, while point-symmetric means that the figure has symmetry around a central point. These two types of symmetry are mutually exclusive, as a figure cannot have both rotational symmetry around an axis and symmetry around a central point simultaneously. **

Diving goggles are not allowed in the swimming pool because they are designed for use in deep water and can obstruct peripheral vision, increasing the risk of collisions with other swimmers. Additionally, diving goggles are not necessary for swimming laps or recreational swimming in a pool with clear water. The use of diving goggles in a swimming pool can also create a safety hazard if the wearer dives into shallow water thinking it is deeper than it actually is. **

No, a rational function cannot be both axisymmetric and point-symmetric. Axisymmetric means that the function is symmetric with respect to rotation around an axis, while point-symmetric means that the function is symmetric with respect to reflection across a point. These two types of symmetry are not compatible with each other, so a function cannot exhibit both types of symmetry simultaneously. **

The derivative of an axisymmetric function is always point-symmetric because the function has the same value at every point along a given radius from the axis of symmetry. This means that the rate of change of the function with respect to the distance from the axis is the same in all directions, resulting in a point-symmetric derivative. In other words, the derivative of an axisymmetric function is the same in all directions, leading to point-symmetry. **