Question

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

ad =
de =
bc =

Explanation:

Step1: Find the length of AD

Since D is the mid - point of AB and $AB=5.4$, then $AD=\frac{AB}{2}=\frac{5.4}{2}=2.7$.

Step2: Find the length of DE

The length of a mid - segment of a triangle (DE) is half the length of the third side (BC). Given $AC = 12.6$, and DE is parallel to BC and half of it. So $DE=\frac{AC}{2}=\frac{12.6}{2}=6.3$.

Step3: Find the length of BC

By the mid - segment theorem, the mid - segment (DE) is parallel to the third side (BC) and its length is half of BC. So $BC = 2\times DE$. Since $DE = 6.3$, then $BC=12.6$.

Answer:

$AD = 2.7$, $DE = 6.3$, $BC = 12.6$