195. Given a tetrahedron $A B C D$. In the planes defining its faces, points $A_{i}, B_{i}, C_{i}, D_{i}$ are taken such that the lines $A A_{i}, B B_{i}, C C_{i}, D D_{i}$ are parallel to each other. Find the ratio of the volumes of the tetrahedrons $A B C D$ and $A_{1} B_{1} C_{1} D_{\mathrm{i}}$.
195. Let $M$ be the point of intersection of the lines $C B_{1}$ and $C_{1} B$. The vertex $A$ lies on $D M$. We draw a plane through the points $D, D_{1}$, and $A$. Denote by $K$ and $L$ its points of intersection with $C_{1} B_{i}$ and $C B$, and by $A_{2}$ the point of intersection of the line $A A_{\hat{1}}$ with $D_{\mathrm{i}} K$ (Fig. 43). From the fact that ${ }^{A_{2}} C_{1} B_{1} B$ is a trapezoid and $K L$ passes through the intersection of its diagonals, it follows that $|K M|=|M L|$. Further, considering the trapezoid $D_{\mathrm{i}} K L D$, we will prove that $\left|A A_{1}\right|=\frac{1}{2}\left|A A_{2}\right|$. Therefore,

$$
v_{A B C D}=\frac{1}{3} v_{A_{2} B C D}
$$

But from the previous problem, it follows that $V_{A_{2} B C D}=V_{A_{1} B_{1} C_{1} D_{1}}$. Thus, the ratio of the volumes of the pyramids $A_{1} B_{1} C_{1} D_{i}$ and $A B C D$ is 3.