If two straight lines are perpendicular to the same line, prove that they are parallel to each other.
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let the slope of the two lines be m₁ and m₂.
let the slope of the line on which they are perpendicular be m.
m₁ m = -1 ........[1]
m₂ m = -1.........[2]
from [1] and [2]....
m₁ ( -1/m₂) = -1
m₁ 1/m₂ = 1
m₁ = m₂
∴ from the relation we can conclude that the two lines are parallel to each other
let the slope of the line on which they are perpendicular be m.
m₁ m = -1 ........[1]
m₂ m = -1.........[2]
from [1] and [2]....
m₁ ( -1/m₂) = -1
m₁ 1/m₂ = 1
m₁ = m₂
∴ from the relation we can conclude that the two lines are parallel to each other
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Answer:
they are parallel
Step-by-step explanation:
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