Mathematics

Use the following figure to find: 
$$ GE $$, if $$ FE= 4 $$ cm


ANSWER

8 cm


SOLUTION
In $$\triangle CEG$$ and $$\triangle DEF$$,
$$\angle CEG = \angle DEF $$ (Common angle)
$$\angle ECG =\angle EDF$$ (Corresponding angles, since BD || AE)
$$\angle EGC =\angle EFD$$ (Corresponding angles, since BD || AE)
Hence, $$\triangle CEG \sim \triangle DEF$$, 
Thus, $$\frac{GE}{FE} = \frac{CE}{DE}$$
$$\frac{GE}{FE} = \frac{CD + DE}{DE} $$ (Given, CD = DE)
$$\frac{GE}{4} =  2 $$
$$GE = 8 cm$$
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