Question

prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also​

Answer 1

Step-by-step explanation:

Given:

• A line is perpendicular to one of the two parallel lines.

To Prove:

• The line is also perpendiculal to other line.

Proof: Suppose that lines m and n are parallel to each other and line L is transversal.

[ Mark points A & B on line m ,C & D on line n and P & Q on transversal line L. ]

Here,

• Line L intersects the two parallel line m and n at point K & L respectively.

Since, Line L is perpendicular to line m therefore,

➙ ∠PKB = 90°

Also, PQ intersects parallel lines AB & CD at points K & L respectively.

$\implies{\rm }$ ∠PKB = ∠KLD {Corresponding angles}

$\implies{\rm }$ ∠KLD = 90°

Hence, line L is perpendicular to line n.

Answer 2

Step-by-step explanation:

Given:

A line is perpendicular to one of the two parallel lines.

To Prove:

The line is also perpendiculal to other line.

Proof: Suppose that lines m and n are parallel to each other and line L is transversal.

[ Mark points A & B on line m ,C & D on line n and P & Q on transversal line L. ]

Here,

Line L intersects the two parallel line m and n at point K & L respectively.

Since, Line L is perpendicular to line m therefore,

➙ ∠PKB = 90°

Also, PQ intersects parallel lines AB & CD at points K & L respectively.

⟹ ∠PKB = ∠KLD {Corresponding angles}

⟹ ∠KLD = 90°

Hence, line L is perpendicular to line n.