How to do this? Mathematics in the eighth grade.

(1) Prove: Because BF is perpendicular to CE at point F.

So BFC angle =90 degrees.

Because angle BFC+ angle BCE+ angle CBF= 180 degrees.

So CBF angle BCE angle =90 degrees.

Because angle ACB= angle ACE+ angle BCE=90 degrees.

So angle ACE= angle CBF

Because AC=BC

So the triangle ABC is an isosceles right triangle.

Because d is the midpoint of AB

So CD is the center line and angle bisector of isosceles right triangle ABC.

So the angle CAE=45 degrees.

Angle ACD= Angle BCG= 1. /2 angle ACB=45 degrees.

So angle CAE= angle BCG=45 degrees.

So triangle ACE and triangle CBG are congruent (ASA (

So AE=CG

(2)CM=BE

Proof: because AH is perpendicular to CE and H.

So angle CHM=90 degrees.

Because CD is the center line of isosceles right triangle ABC (proved)

So CD is the perpendicular and bisector of the isosceles right triangle ABC.

So CDE angle =90 degrees.

Angle ACM= 1/2 Angle ACB=45 degrees.

Angle CBE=45 degrees

So angle ACM= angle CBE=45 degrees.

Because CDE angle +CEB angle +DCE angle = 180 degrees.

So DCE angle +CEB angle =90 degrees.

Because angle CHM+ angle M+ angle DCE= 180 degrees.

So angle DCE+ angle M=90 degrees.

So angle M= angle CEB

Because AC=BC

So triangle ACM and triangle CBE are congruent (AAS)

So CM=BE