Mathematics

The key insight is recognizing that $EF$ is a midsegment of triangle $ABD$—it connects the midpoints of two sides. By the midsegment theorem, a segment joining the midpoints of two sides of a triangle is parallel to the third side and exactly half its length. Since $E$ and $F$ are midpoints of $AB$ and $AD$, segment $EF$ is parallel to $BD$ and measures half of it.

The key insight is recognizing that $EF$ is a midsegment of triangle $ABD$—it connects the midpoints of two sides. By the midsegment theorem, a segment joining the midpoints of two sides of a triangle is parallel to the third side and exactly half its length. Since $E$ and $F$ are midpoints of $AB$ and $AD$, segment $EF$ is parallel to $BD$ and measures half of it.