Question

ABC and DBC are two isosceles triangles on the same base BC.show that angleABD is equal angle ACD.

Answer 1

in triangle ABC
angle ABC = angle ACB
since angles opposite to equal sides are equal and also a property of isosceles triangle
in the same way
in triangle DBC
angle DBC = angle DCB

now

in triangle ABC & triangle DBC
         angle ABC = angle DBC
          BC = BC         since common side
         angle ACB = angle DCB
therefore     triangle ABC is congruent to triangle DBC    by ASA congruency
 
now

angle ABD = angle ABC + angle DBC
angle ACD = angle ACB + angle DCB 
since angles ----- ABC = ACB = DBC = DCB
angle ABD = ACD...........
COMPLETED