Question

1. given that segment de is a mid - segment of δabc, find the following. ad = de =

Explanation:

Step1: Recall mid - segment property for $AD$

A mid - segment divides a side in half. Since $AB = 13$ and $D$ is the mid - point of $AB$ (because $DE$ is a mid - segment), then $AD=\frac{AB}{2}$.
$AD=\frac{13}{2}=6.5$

Step2: Recall mid - segment property for $DE$

The length of a mid - segment of a triangle is half the length of the third side. Since $AC = 10$ and $DE$ is a mid - segment parallel to $AC$, then $DE=\frac{AC}{2}$.
$DE=\frac{10}{2}=5$

Answer:

$AD = 6.5$, $DE = 5$