In △ ABC, ab = 5, AC = 3, ad is the middle line on the edge of BC, then the value range of ad is______ ．

In △ ABC, ab = 5, AC = 3, ad is the middle line on the edge of BC, then the value range of ad is______ ．

As shown in the figure, extend ad to e, so that de = ad, ≌ ad is the middle line on the edge of BC, ≌ BD = CD, in △ abd and △ ECD, BD = CD ∠ ADB = EDC (equal to vertex angle), de = ad, ≌ abd ≌ ECD (SAS), ≌ CE = AB, ≌ AB = 5, AC = 3, ≌ 5-3 ＜ AE ＜ 5 + 3, i.e. 2 ＜ AE ＜ 8, 1 ＜ ad ＜ 4

In triangle ABC, AC = 5, midline ad = 4, find the value range of edge ab

Solution: extend ad to E,
Let de = ad = 4,
If be and CE are connected, the quadrilateral ABEC is a parallelogram
CE=AB
According to the sum of the two sides of the triangle is greater than the third side, the difference between the two sides is less than the third side
AB + 5 > 8,
AB