In the figure given below ABC is a triangle with AB BC and D is an interior point of the triangle AB...........

Quantitative Aptitude (CDS) Coordinate Geometry

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

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 and 2 only

2 and 3 only

1 and 3 only

1, 2 and 3

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Explanation:

As, ∠DAC = ∠DCA
So, DA = DC
Hence triangle ADC is an isosceles triangle
Hence statement 1 is correct.
Statement 2:
As, we know that, the centroid of a triangle is the point where the three medians of the triangle meet.
Hence statement 2 is incorrect.
Statement 3:
AB = CB
AD = DC
BD = BD
Thus, triangle ABD ≅ triangle CBD [By, SSS congruence criteria]
Hence statement 3 is correct.
Hence option (3)