Question

Is there enough information to conclude that the two triangles are congruent? If so, what is a correct congruence statement?

Answer 1

Yes,it can be proved to be congruent,as:

AB=AD (given)
AC=AC (given)
Since AB = AD,it is an isosceles △
Thus,BC=CD(properties of isos.△)

Therefore,ΔCAB  ≅ ΔDAC (SSS)

The answer is Yes;ΔCAB  ≅ ΔDAC

Hope it helps!

Answer 2

Answer: Yes,  Δ ACB  ≅ Δ ACD

Step-by-step explanation:

Since, Here ABD is a triangle in which AB = AD

Therefore, ABD is the isosceles triangle,

Also, AC is altitude of the  isosceles triangle ABD.

Therefore, AC will be the median of the triangle ABC ( By the property of isosceles triangle )

Thus, BC = CD

Now, In Δ ACB and Δ ACD,

AB ≅ AD (given)

CB≅CD ( Because CB= CD)

And, AC≅AC  ( Reflexive)

Therefore By SSS postulate of congruence,

Δ ACB ≅Δ ACD

Thus, Third Option is correct.