Question
In Fig. show that
  1. $AB || CD$
  2. $EF || GH$

Answer

  1. From the given figure,
$\angle\text{CIF}+\angle\text{FIJ}=180^\circ$ [Liner pair]
$\Rightarrow\angle\text{CIF}=180^\circ-\angle\text{FIJ}=180^\circ-50^\circ=130^\circ$

Now, $\angle\text{ALI}+\angle\text{CIF}=130^\circ$
$\therefore \text{ AB }|| \text{ CD}$ as their corresponding angles are equal.
  1. From the given figure,
$\angle\text{GKL}+\angle\text{LKJ}=180^\circ$ [Liner pair]
$\Rightarrow\angle\text{LKJ}=180^\circ-\angle\text{GKL}=180^\circ-50^\circ=130^\circ$
Now, $\angle\text{ALI}+\angle\text{LKJ}=130^\circ$
$\therefore \text{ EF }|| \text{ GH}$ as their corresponding angles are equal.

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