The ninth grade of Beijing Normal University proved the rectangular geometry problem last semester.

(1) Proof: Because AB=AC

So triangle ABC is an isosceles triangle

Because AD is perpendicular to BC and D.

So AD is the perpendicular, median and angular bisector of isosceles triangle ABC.

So the angle ADC=90 degrees.

BD=CD

Angle BAD= angle CAD= 1/2 angle BAC

Because AN is the bisector of the external angle cam with angle BAC.

So the angle can be = angle person = 1/2 angle cam.

Because angle BAC+ angle CAM= 180 degrees

So angle CAD+ angle CAN= angle DAN=90 degrees.

Because CE is perpendicular to AN and e.

So the angle AEC=90 degrees

Because angle ADC+ angle DAE+ angle AEC+ angle DCE=360 degrees.

So DCE angle =90 degrees

Therefore, angle ADC= angle DCE= angle AEC= angle DAE=90 degrees.

So the quadrilateral ADCE is a rectangle.

(2) The quadrilateral ABDE is a parallelogram.

Proof: Because the quadrilateral ADCE is a rectangle.

So AE=DC

AE parallel DC

Because BD=CD (authentication)

So AE=BD

So the quadrilateral ABDE is a parallelogram.

(3)DF= 1/2AB

Proof: Because the quadrilateral ADCE is a rectangle.

So AC=DE

DF=EF= 1/2DE

So DF= 1/2AC.

Because AB=AC

So DF= 1/2AB.