Question

Find DF, if CG = 11 cm

• A. $5.6cm$
• B. $5.5cm$
• C. $0.55cm$
• D. $6cm$

Answer 1

The correct option is B $5.5cm$

In $△CEG$ and $△DEF$,
$\angle CEG=\angle DEF$ (Common angle)
$\angle ECG=\angle EDF$ (Corresponding angles, since BD || AE)
$\angle EGC=\angle EFD$ (Corresponding angles, since BD || AE)
Hence, $△CEG\sim △DEF$, BY AAA
Thus, $\frac{DF}{CG}=\frac{DE}{CE}$
$\frac{DF}{11}=\frac{DE}{DE+CD}$ (Given, CD = DE)
$\frac{DE}{11}=\frac{1}{2}$
$DE=5.5cm$