Question

If AD is a median of triangle ABC and DE ll BA. Show that BE is also a median of triangle ABC.

Answer 1

Answer on Question #48127 – Math – Geometry

If AD is a median of triangle ABC and DE II BA. Show that BE is also a median of triangle ABC.

Solution

$\Delta ABC \sim \Delta ECD$ (AAA).

So, $\frac{BC}{DC} = \frac{AC}{CE}$ .

$$AD \text{ - median} \rightarrow \frac{BC}{DC} = 2 \rightarrow \frac{AC}{CE} = 2 \rightarrow CE = \frac{AC}{2}.$$

Thus, $BE$ - median.

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