If a transversal line intersects two parallel lines, then each pair of corresponding angles are ____.

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Detailed Solution

If a transversal line intersects two parallel lines, then each pair of corresponding angles are equal.
Given, a transversal line intersects two parallel lines.
Assume that there are two parallel lines

p & q

and a transversal line passing through them. The figure is as shown below:
Question Image

In this figure,

∠ 1

and

∠ 2

are corresponding angles.
Given,

p ∥ q

⇒ ∠ 2 = ∠ 3

(Alternate interior angles) ___________(1)

⇒ ∠ 3 = ∠ 1

(Vertically opposite angles) __________(2)
Comparing the equations (1) and (2),

⇒ ∠ 1 = ∠ 2

Since,

∠ 1

and

∠ 2

are corresponding angles.
Therefore, corresponding angles are equal.
Hence, if a transversal line intersects two parallel lines then each pair of corresponding angles are equal.
Therefore, the correct answer is equal.

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