5. ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.
Solution: In the question, it is given that ABC and DBC are two isosceles triangles. We will have to show that ∠ABD = ∠ACD Proof: Triangles ΔABD and ΔACD are similar by SSS congruency since AD = AD (It is the common arm) AB = AC (Since ABC is an isosceles triangle) BD = CD (Since BCD is an isosceles triangle) So, ΔABD ≅ ΔACD. ∴ ∠ABD = ∠ACD by CPCT.
