Question 111

In the given figure, Find out which pair of lines are parallel.

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Solution

From the given figure,
$∠ 1 = 180^{\circ} - 123^{\circ} \Rightarrow ∠ 1 = 57^{\circ}$
Also $∠ 2 = 180^{\circ} - 57^{\circ} \Rightarrow ∠ 2 = 123^{\circ}$
Now, $∠ 1 + ∠ 2 = 57^{\circ} + 123^{\circ} = 180^{\circ} I f s u m o f t h e c o n s e c u t i v e a n g l e s a r e 180^{\circ} t h e n t h e l i n e s a r e p a r a l l e l .$
$∴ E F | | G H$
$N o w, ∠ 3 = 180^{\circ} - ∠ 2 \Rightarrow ∠ 3 = 180^{\circ} - 123^{\circ} = 57^{\circ}$
Also, $∠ 4 = 180^{\circ} - 55^{\circ} = 125^{\circ} ∴ ∠ 3 + ∠ 4 = 57^{\circ} + 125^{\circ} = 182^{\circ} \neq 180^{\circ}$
So, GH and KP are not parallel.
$A l s o, ∠ 3 + 122^{\circ} = 57^{\circ} + 122^{\circ} = 179^{\circ} \neq 180^{\circ} H e n c e, A B a n d C D a r e n o t p a r a l l e l .$

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Question 109

In the given figure state which pair of lines are parallel. Give reason.

Question 110(ii)

In the given figure, examine whether the following pairs of lines are parallel or not.

Δ A B C ≅ Δ C D A .

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