Mathematics

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


SOLUTION
Consider $$\triangle EFG$$ and $$\triangle GCD$$
$$EF\parallel CD\implies \angle GCD=\angle GEF\ (\because $$ 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 
$$\triangle EFG\sim \triangle CDG$$
$$\implies \dfrac{EF}{EG}=\dfrac{CG}{CD}\implies EF=5\times \dfrac{18}{10}=9\ cm$$
$$AB\parallel EF\implies \angle BAC=\angle FEC,\angle ABC=\angle EFC$$ and $$\angle C$$ remains the same
So by AAA criteria ,we get 
$$\triangle  ABC\sim \triangle EFC$$
$$\implies \dfrac{AC}{AB}=\dfrac{EC}{EF}\implies AC=15\times \dfrac{15}{9}=25\ cm$$ 
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Subjective Medium Published on 09th 09, 2020
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