Isosceles Triangle: Calculate ∠BAD Using Height Properties

In $\triangle ABC$, since $AB = AC$, the triangle is isosceles, and the base angles $\angle ABC$ and $\angle ACB$ are equal. Given that $\angle BAC = 70^{\circ}$, the sum of the angles in a triangle is $180^{\circ}$.
Therefore, the two base angles together are $180^{\circ} - 70^{\circ} = 110^{\circ}$.
Since these angles are equal, each is $\frac{110^{\circ}}{2} = 55^{\circ}$.

Since $AD$ is the height from $A$ to $BC$, it bisects $\angle BAC$.
Thus, $\angle BAD = \frac{\angle BAC}{2} = \frac{70^{\circ}}{2} = 35^{\circ}$.

Therefore, the size of $\angle BAD$ is $\textbf{35 degrees}$.