Question

In the figure given below, $AB,EF$ and $CD$ are parallel lines. Given that $AB=15cm,EG=5cm,GC=10cm$ and $DC=18cm$. Calculate
(i) $EF$
(ii) $AC$.

Answer 1

Consider $△EFG$ and $△GCD$

$EF\parallel CD⟹\angle GCD=\angle GEF(\because$ alternative angles $)$

$\angle FGE=\angle CGD(\because$ vertically opposite angles $)$

as two angles are equal automatically third angle will be equal

So by AAA criteria , we get

$△EFG\sim △CDG$

$⟹\frac{EF}{EG}=\frac{CG}{CD}⟹EF=5\times \frac{18}{10}=9cm$

$AB\parallel EF⟹\angle BAC=\angle FEC,\angle ABC=\angle EFC$ and $\angle C$ remains the same

So by AAA criteria ,we get

$△ABC\sim △EFC$

$⟹\frac{AC}{AB}=\frac{EC}{EF}⟹AC=15\times \frac{15}{9}=25cm$