Some doubts and new properties (for me) I found regarding the properties of some geometric shapes:

1. The median of a trapezoid is the line joining the midpoint of the two legs (the non-parallel sides). Yet, it can be calculated as the average of the two bases (the parallel sides).

2. The diagonals of a square bisect the angles. Does this apply to rhombus and rectangle too (or, parallelograms in general)?

3. The diagonals of a square and a rhombus bisect each other at 90 degrees. Does this apply to a rectangle too (or, parallelograms in general)?

4. The diagonals of a square are equal. If the diagonals of a rhombus are equal, it must be a square. Does this apply to a rectangle too (or, parallelograms in general)?

5. Does the altitude of an isosceles triangle bisect the base (the non-equal side)?

6. Does the altitude of the base (non-equal side) of an isosceles triangle bisect the vertex?

7. Do (5) and (6) apply to an equilateral triangle?

I would be thankful if the doubts were cleared off (or is it cleared away?).

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