# Thread: Midpoints in a Triangle

1. ## Midpoints in a Triangle

in triangle ABC let points D and E be the midpoints of sides AB and AC. Show DE must be half the length of BC.

Thank you,
mdk

2. Originally Posted by mdk

in triangle ABC let points D and E be the midpoints of sides AB and AC. Show DE must be half the length of BC.

Thank you,
mdk
$\triangle ABC$ is congruent to $\triangle ADE$, then we have

$\frac{AD}{AB} = \frac{DE}{BC}$

$\frac{1/2 AB}{AB} = \frac{DE}{BC}$

$DE = \frac{1}{2}BC$