prove that the two lines I that are respectively perpendicular to two parallel lines and are parallel to each other.
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Two line are respectively perpendicular to two parallel lines. Show that they are parallel to each other.
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Take two parallei lines 'l' and 'm'Take another two lines 'p' and 'q' such that p⊥l and q⊥m.
It is required to prove that the lines p and q are parallel to each other.The figure is shown below: (Check this attachment) ☺️
Note that q⊥m which implies that ∠1=90°and p⊥l which implies that ∠2=90°.
It is given that, l∥m, so that the sum of interior angles on same side of transversal is 180°.
This implies that,
∠2+ ∠4=180°
90°+ ∠4=180°
∠4=180°−90°
∠4=90°
Now ∠1 and ∠4 are corresponding angles formed by the lines 'p' and 'q' taking 'm' as transversal and both are equal (each 90°).
This shows that the lines 'p' and 'q' are parallel to each other.Hence it is proved that if two lines are perpendicular to two parallel lines, then they are parallel to each other.
Hope it helps...!!!!
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Take two parallei lines 'l' and 'm'Take another two lines 'p' and 'q' such that p⊥l and q⊥m.
It is required to prove that the lines p and q are parallel to each other.The figure is shown below: (Check this attachment) ☺️
Note that q⊥m which implies that ∠1=90°and p⊥l which implies that ∠2=90°.
It is given that, l∥m, so that the sum of interior angles on same side of transversal is 180°.
This implies that,
∠2+ ∠4=180°
90°+ ∠4=180°
∠4=180°−90°
∠4=90°
Now ∠1 and ∠4 are corresponding angles formed by the lines 'p' and 'q' taking 'm' as transversal and both are equal (each 90°).
This shows that the lines 'p' and 'q' are parallel to each other.Hence it is proved that if two lines are perpendicular to two parallel lines, then they are parallel to each other.