Question 112(i)

In the given figure, show that
AB || CD

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Solution

From the given figure,
$∠ C I F + ∠ F I J = 180^{\circ} \Rightarrow ∠ C I F + 180^{\circ} - ∠ F I J = 180^{\circ} - 50^{\circ} = 130^{\circ}$

Now, $∠ A L I = ∠ C I F = 130^{\circ}$
$∴ A B | | C D$ as their corresponding angles are equal.

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Question 152 (ii)

In the given figure, $∠ 1 = ∠ 2$ and $∠ 3 = ∠ 4$
Show that AD = AB and CD = CB

In the given figure, show that AB || CD

∠ C = ∠ D

A H > A B + B C + C D

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