Question

Given the above, which method would you use to prove ABD ≅ ACD? AAS SSS ASA The two triangles are not congruent.

Answer 1

Yes they are congruent by SSS

AB = AC because triangle ABC is isosceles

BD = CD because triangle BDC is isosceles

AD is common to both triangles


conguent by SSS

Answer 2

SSS rule of congruency

Explanation:

It is given that ΔABC is isosceles triangle and ΔBDC is also isosceles triangle.

Thus, AB=AC and BD=DC.

Now, consider ΔABD and ΔACD, we have

AB=AC (Because ΔABC is isosceles triangle)

AD=AD(Common side of both triangles)

BD=DC(Because ΔBDC is isosceles triangle)

Therefore, by SSS congruency rule,

ΔABD≅ΔACD

Hence proved.