Question

In the given figure , BD and CE are altitudes on side AC and AB respectively. Is triangle BCD congruent to triangle CBE ?

Answer 1

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)