Question

in the figure below, points d, e, and f are the midpoints of the sides of △abc. suppose df = 34, ac = 36, and bc = 72. find the following lengths. ab = de = be =

Explanation:

Step1: Find AB via Midsegment Theorem

The midsegment $DF$ is half of $AB$.
$AB = 2 \times DF = 2 \times 34 = 68$

Step2: Find DE via Midsegment Theorem

The midsegment $DE$ is half of $BC$.
$DE = \frac{1}{2} \times BC = \frac{1}{2} \times 72 = 36$

Step3: Find BE via Midpoint Definition

$E$ is the midpoint of $AB$, so $BE$ is half of $AB$.
$BE = \frac{1}{2} \times AB = \frac{1}{2} \times 68 = 34$

Answer:

$AB = 68$
$DE = 36$
$BE = 34$