In the given figure, the ratio ABD : ACD is

The figure shows a triangle ABC with an interior point D. The markings on the sides indicate the following equalities:

• AB = AC (indicated by a single tick mark on both sides)
• BD = CD (indicated by a double tick mark on both sides)

Consider the two triangles $\triangle ABD$ and $\triangle ACD$.
We have:

• AB = AC (Given from the markings)
• BD = CD (Given from the markings)
• AD = AD (Common side to both triangles)

Since all three corresponding sides of $\triangle ABD$ and $\triangle ACD$ are equal, the triangles are congruent by the Side-Side-Side (SSS) congruence criterion.
Therefore, $\triangle ABD \cong \triangle ACD$.

When two triangles are congruent, their corresponding angles are equal.
Thus, $\angle ABD = \angle ACD$.

Since $\angle ABD = \angle ACD$, the ratio $\angle ABD : \angle ACD$ is $1:1$.