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:

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

Which of the above statements are correct?

  1. 1 and 2 only
  2. 2 and 3 only
  3. 1 and 3 only
  4. 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.