It is known that point B is a point on the line AC, D is the midpoint of AC, e is the midpoint of AB, BC = 6. (1) draw a graph and find the length of de; (2) if (1) midpoint B is a point on the extension line of AC, other conditions remain unchanged, draw a graph and find the length of de

It is known that point B is a point on the line AC, D is the midpoint of AC, e is the midpoint of AB, BC = 6. (1) draw a graph and find the length of de; (2) if (1) midpoint B is a point on the extension line of AC, other conditions remain unchanged, draw a graph and find the length of de

(1) As shown in Figure 1, let AE = x, BD = y, then be = x, ∵ d be the midpoint of AC, ∵ ad = CD, namely AE + be + BD = CD, and BC = 6, x + X + y = 6-y, ∵ x + y = 3, namely de = 3; (2) let de = x, CE = y, then ad = DC = x + y, ∵ e be the midpoint of AB, ∵ AD + de = EC + BC, namely x + y + x = y + 6, ∵ x = 3, namely de = 3

As shown in the figure, it is known that De is the vertical bisector of AB, FG is the vertical bisector of AC, points E and G are on BC, BC = 10cm, and the perimeter of triangle AEG is calculated

∵ De is the vertical bisector of ab
∴AE=BE
∵ FG is the vertical bisector of AC
∴AG=CG
The perimeter of ∧ AEG
=AE+AG+EG
=BE+CG+EG
=BC
=10cm
The perimeter of the AEG is 10 cm

As shown in the figure, in the triangle ABC, ab = AC, the vertical bisector of AB intersects AC at point E. given that the perimeter of the triangle ABC is 8, ac-bc = 2, find
The length of AB and BC

As shown in the figure, in the triangle ABC, ab = AC, the vertical bisector of AB intersects point D, AC intersects point E. given that the perimeter of triangle BCE is 8, ac-bc = 2, find ab
The vertical bisector of ∵ AB intersects at point E
∴BE=AE
∴BE+BC+CE=AE+CE+BC=AC+BC=8
That is, AC + BC = 8
∵AC-BC=2
∴AC=5
BC=3