Two lines are respectively perpendicular to two parallel lines. Then these lines to
each other are
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intersecting lines
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Answer:
Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.
Step-by-step explanation:
According to the figure consider the two parallel lines as m and n
We know that p ⊥ m and q ⊥ n
So we get
∠1 = ∠2 = 90
We know that m || n and p is a transversal
From the figure we know that ∠1 and ∠3 are corresponding angles
So we get
∠1 = ∠3
We also know that
∠2 = ∠3 = 90
We know that ∠2 and ∠3 are corresponding angles when the transversal n cuts p and q.
So we get p || q.
Therefore, it is shown that the two lines which are perpendicular to two parallel lines are parallel to each other.
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