Let $M$ be the midpoint of side $B C$ of parallelogram $A B C D$. In what ratio does segment $A M$ divide diagonal $B D$?
Consider similar triangles.

## Solution

Let $K$ be the point of intersection of segments $A M$ and $B D$. Triangles $B K M$ and $D K A$ are similar (by two angles) with a similarity ratio of $B M: A D = 1: 2$. Therefore, $B K: K D = 1: 2$.

![](https://cdn.mathpix.com/cropped/2024_05_06_4fce0705b02fa9e106d4g-17.jpg?height=368&width=943&top_left_y=2463&top_left_x=566)

## Answer

## Problem