Therefore, angle ADB= angle BDF= angle ADC=90 degrees.
Because angle ABC+ angle ADB+ angle BAD= 180 degrees.
Angle ABC=45 degrees
So the angle BAD=45 degrees
So angle BAC= angle BAD=45 degrees.
So AD=BD
Because BE is perpendicular to AC and e.
So BEC angle =90 degrees.
Because angle BEC+ angle ACD+ angle CBE= 180 degrees.
So angle ACD+ angle CBE=90 degrees.
Because angle CBE+ angle BFD+ angle BDF= 180 degrees.
So angle CBE+ angle BFD=90 degrees.
So angle BFD= angle ACD
Angle BDF= angle ADC=90 degrees
So triangular BDF and triangular ADC are congruent (AAS)
So DF=DC
So the triangle CDF is an isosceles triangle
Because angle ADC= angle CDF=90 degrees
So the angle CDF=90 degrees.
So the triangle CDF is an isosceles right triangle.
(2) Proof: Because AD is perpendicular to BC and D ..
So angle ADB= angle BDF= angle CDA=90 degrees.
Because angle ABC+ angle ADB+ angle BAD= 180 degrees.
Angle ABC=45 degrees
So the angle BAD=45 degrees
So angle BAD= angle ABC=45 degrees.
So AD=BD
Because angle ADC+ angle CAD+ angle ACB= 180 degrees.
So angle ACB+ angle CAD=90 degrees.
BeCAuse BE is perpendicular to AC, the extension line of ca is in e.
So BEC angle =90 degrees.
Because BEC angle +FBD angle +ACB angle = 180 degrees.
So FBD angle +ACB angle =90 degrees.
So angle FBD= angle CAD
Angle BDF= angle ADC=90 degrees
So triangular BDF and triangular ADC are congruent (AAS)
So DF=CD
Because angle ADC= angle CDF
So the angle CDF=90 degrees.
So the triangle CDF is an isosceles right triangle.