It is known that ad is the middle line on the ABC side and BC side of the triangle, ab = 12 and AC = 8. The value range of ad is obtained

CE / / AB, EC / / AC
Abce parallelogram
D is its diagonal intersection
In the triangle AEB, AE = 2ad, ab = 12, EB = AC = 8
AB+EB>AE>AB-EB
That is 12 + 8 > 2ad > 12-8
10>AD>2

In △ ABC, ad ⊥ BC in D, de ⊥ AB in E, DF ⊥ AC in F

It is proved that in △ abd and △ ade, the two right triangles are similar from ∠ bad = ∠ DAE,
There are: AE / ad = ad / AB, that is AE * AB = ad & # 178;
Similarly, right angle △ ADC is similar to right angle △ ADF, and ac * AF = ad & # 178 is obtained;
So: AE * AB = af * AC
Namely: AE / AF = AC / AB
It's this picture, not this one

As shown in the figure, in △ ABC, ab = AC, D is the midpoint of BC, connecting ad.de ⊥ AB, DF ⊥ AC, e and F are perpendicular feet. How many pairs of congruent triangles are there in the figure? Please mark them separately with "≌"

There are three pairs. (1) △ abd ≌ △ ACD; △ ade ≌ △ ADF; △ BDE ≌ △ CDF. It is proved that:

It is known that ad is the middle line on the ABC side and BC side of the triangle, ab = 12 and AC = 8. The value range of ad is obtained