# ABC is a triangle with AB = BC and D is an interior point

Geometry
In the figure given below, ABC is a triangle with AB = BC and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA.

Consider the following statements:

- Triangle ADC is an isosceles triangle.
- D is the centroid of the triangle ABC.
- Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3

### Answer

Since ∠DAC = ∠DCA, AD = CD. Therefore, triangle ADC is an isosceles triangle.

Triangle ABD is congruent to the triangle CBD by SSS Rule.

The centroid of a triangle is the centre of the triangle that is the point of intersection of all the three medians of a triangle.

**The correct option is D.**