The midpoints of the sides of a triangle with area $T$ are joined to form a triangle with area $M$. What is the ratio of $M$ to $T$? Express your answer as a common fraction.
I recall a theorem that says that if you join the midpoints of the sides of a triangle, you get a smaller triangle that is similar to the original one and has half the length of each side. This means that the smaller triangle has a scale factor of $\frac{1}{2}$ compared to the original one. I also remember that the area of a similar figure is proportional to the square of the scale factor. So, if the smaller triangle has a scale factor of $\frac{1}{2}$, its area must be $\frac{1}{4}$ of the area of the original triangle. Therefore, the ratio of $M$ to $T$ is $\frac{1}{4}$. 