ABC is a triangle in which altitudes BD and CE to sides AC and AB respectively are equal .  Show that 
(a) triangle BCD congruence to triangle CBE
​(b)  AB =AC
 

In triangle ABD and triangle ACE,
           angle A = angle A  (common angle)
          angle ADB = angle AEC (Each 90)
          BD = CE (given)
Therefore, triangle ABD congruent to triangle ACE {AAS)

       AB = AC (c.p.c.t.)
Therefore, angle B = angle C (isosceles triangle property)

In triangle BCD and triangle CBE
angle BDC = CEB (90)
angle B = C 
BC = BC (common side)

therefore bcd congruent to cbe (aas)