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Does the mean of triangle bisect the area of triangle?
The answer depends on what you mean by "mean of triangle". There is no such geometric term.
Can a form be geometric?
That all depends on what you mean by "form". If you are referring to "shape", then yes it can be geometric. For instance, a triangle is geometric.
What if the altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse?
Always true. To see this draw the circle which passes through the three points of the triangle. Reproduce the reflection of the triangle on the hypotenuse (which passes through the centre). Then use the theorem of intersecting chords of a circle to give the result immediately. It's also simply proved by algebra.
How to find the attitude of a triangle?
If you mean "altitude", and by that you mean the height of the top of the triangle above its base, then draw a line from the top of the triangle to the base, at right angles to the base, and measure that line. Alternately, the height of a triangle above its base is twice the area divided by the base length.
What does a triangle with a square inside mean?
It means that it is a right angle triangle
