Question

In $\Delta ABC$, a line DE is drawn joining the midpoints of AB and BC. Which of the following statements is true?

• A. DE intersects AC outside $\Delta$ ABC
• B. DE is parallel to BC
• C. DE is parallel to AC
• D. DE intersects AC inside $\Delta$ ABC

Answer 1

The correct option is C

DE is parallel to AC

Given D and E are midpoints of AB and BC respectively.
$\Rightarrow AD=DB$ and $BE=EC$
$\Rightarrow \frac{AD}{DB}=1=\frac{BE}{EC}$
From Converse of Basic Proportionality Theorem, $DE\parallel AC$ .
So, the line DE never intersects AC.