As shown in the figure, in the square ABCD with side length of 8, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB with G, intersect CD with H. if cm = 2, then GH=______ ．

As shown in the figure, in the square ABCD with side length of 8, M is a point on BC. Connect am, make the vertical bisector GH of am, intersect AB with G, intersect CD with H. if cm = 2, then GH=______ ．

According to Pythagorean theorem, am = AB2 + BM2 = 82 + 62 = 10, as shown in the figure, through point B as BN ‖ GH, then the quadrilateral bnhg is a parallelogram, ∪ BN = GH, ∪ GH is the vertical bisector of am, ∪ CBN + ∠ AMB = 90 ° and ∪ BAM + ∠ AMB = 90 ° and ∪ BAM = ∠ CBN, in △ ABM and △ BCN, ∪ BAM = ∠ cbnab = BC ∠ ABC = 90 ° and ∪ BCN = 90 ° respectively So the answer is: 10