A transversal intersects two given lines in such a way that the interior angles on the same side of the transversal are equal. Show by means of a figure that the lines need not be parallel. State the condition under which the two lines will be parallel.
Here ∠1 = ∠2 ….(Given)
AB will be parallel to CD only when
∠1 + ∠2 = 180° (∠1 and ∠2 should be supplementary) ⇒ 2 ∠1 = 180°
⇒ ∠1 = 90° ⇒ ∠1 = ∠2 = 90°
There AB will be parallel to CD when ∠1 = ∠2 = 90°, but AB will not be parallel to CD if two angle (∠1 and ∠2) are either acute or obtuse.
AB will be parallel to CD only when
∠1 + ∠2 = 180° (∠1 and ∠2 should be supplementary) ⇒ 2 ∠1 = 180°
⇒ ∠1 = 90° ⇒ ∠1 = ∠2 = 90°
There AB will be parallel to CD when ∠1 = ∠2 = 90°, but AB will not be parallel to CD if two angle (∠1 and ∠2) are either acute or obtuse.
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