Mathematics

This is the midpoint theorem in action—a beautiful consequence of similar triangles and proportional sides. Since $DE \parallel BC$, triangles $ADE$ and $ABC$ are similar, which means their corresponding sides are proportional. The key insight is that because $D$ divides $AB$ in the ratio $1:1$ (it's the midpoint), the same ratio must hold for how $E$ divides $AC$. Use the proportionality of similar triangles to show that $AE = EC$.

This is the midpoint theorem in action—a beautiful consequence of similar triangles and proportional sides. Since $DE \parallel BC$, triangles $ADE$ and $ABC$ are similar, which means their corresponding sides are proportional. The key insight is that because $D$ divides $AB$ in the ratio $1:1$ (it's the midpoint), the same ratio must hold for how $E$ divides $AC$. Use the proportionality of similar triangles to show that $AE = EC$.