# ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.

**Solution:**

Given: ABC and DBC are isosceles triangles

To Prove: ∠ABD = ∠ACD

Let's join point A and point B.

In △DAB and △DAC,

AB = AC (Given)

BD = CD (Given)

AD = AD (Common side)

∴ △ ABD ≅ △ ACD (By SSS congruence rule)

∴ ∠ABD = ∠ACD (By CPCT)

**Video Solution:**

## ABC and DBC are two isosceles triangles on the same base BC (see Fig. 7.33). Show that ∠ABD = ∠ACD.

### NCERT Maths Solutions Class 9 - Chapter 7 Exercise 7.2 Question 5:

**Summary:**

If ABC and DBC are two isosceles triangles on the same base BC, then △ ABD ≅ △ ACD by SSS congruence and ∠ABD = ∠ACD.