2. The plane where the square ABCD is located exists (center of gravity or center of gravity), so that the triangle formed by it and each fixed point is an isosceles triangle.
3. In the parallelogram ABCD, DC=2AD, and m is the midpoint of DC, then the AMB angle is equal to (90).
After analyzing that m is MN∑AD, MADN and MNBC are rhombic. AM and BM are diagonal lines of two diamonds,
So AM⊥BM
4.AB = 2, BC=3, and the bisectors of angle B and angle CD in the parallelogram ABCD intersect with AD and EF respectively, then EF = (1).
The analysis proves that △DCF and △ABR are both isosceles △, AE=CF=AB=CD=2.
Therefore, EF=AE+DF-AD=2+2-3= 1.
5. It is known that the two diagonal lines AC = 8cm and BD=6cm of diamond ABCD, so the distance from diagonal line O to either side is equal to (12/5 cm).
The diagonals of the diamond are perpendicular to each other, so the diagonals divide the diamond into four right triangles of equal size.
Because AC=8cm, BD = 6cm；; Therefore, AO=4cm, bo = 3cm；; AB = 5 cm
According to the right triangle area formula,1/2× ao× bo =1/2× ab× h.
Therefore, h =12/5cm.