Question

Triangle ABC&TriangleDBC are two isoceles triangle on the same base BC(see figure).Show that angle ABD = angle ACD

Answer 1

Ex 7.3, 1 - Chapter 7 Class 9 Triangles. ... Ex 7.3,1 ABC and DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see figure ). ... If AD is extended to interest BC at P, show that (iii)AP bisects as well as .

Answer 2

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$\bold\red{Solution:}$

AB=AC                  (Given)

It means that ∠ABC=∠ACB   (In triangle, angles opposite to equal sides are equal) .....(1)

BD=DC             (Given)

It means that ∠DBC=∠DCB    (In triangle, angles opposite to equal sides are equal)  ......(2)

Adding (1) and (2), we get

∠ABC+ ∠DBC=∠ACB+∠DCB

⇒∠ABD=∠ACD

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