Question

Use the following figure to find:

$DF$, if $CG=11$ cm

• A. $5.1$ cm
• B. $4.5$ cm
• C. $6.5$ cm
• D. $5.5$ cm

Answer 1

The correct option is D $5.5$ cm

In $△DEF$ and $△CEG$
$\angle DEF=\angle CEG$ (Common angle)
$\angle EDF=\angle ECG$ (Corresponding angles)
$\angle EFD=\angle EGC$ (Corresponding angles)
Thus, $△DEF\sim △CEG$ (AAA rule)
Thus, $\frac{DE}{CE}=\frac{DF}{CG}$
$\Rightarrow \frac{1}{2}=\frac{DF}{11}$
$\Rightarrow DF=5.5$ cm