If two parallel lines are cut by a transversal, then pair of corresponding angles are equal at Algebra Den

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Home >> Define Line, Line Segment and Rays >> Transversal Line >> Properties / Facts about Transversal of parallel line >> Transversal Property / Fact - (1) >>

If two parallel lines are cut by a transversal, then pair of corresponding angles are equal

Transversal Property / Fact - (1) Transversal Property / Fact - (2) Transversal Property / Fact - (3)

If two parallel lines are cut by a transversal, then each pair of corresponding angles has equal measure.

Explanation:

Draw two parallel lines P and Q as shown in the following diagram

Now, draw a Transversal X to above lines P and Q, as shown in the following diagram.

Mark corresponding ∠ 1 and ∠ 2 as shown in the following diagram:

With the help of trace paper if you trace ∠ 2 and slides it towards ∠ 1, you will notice that both ∠ 1 and ∠ 2 coincides with each other; as shown in the following diagram:

So, this proves that corresponding ∠ 1 = ∠ 2.
And similarly all other pairs of corresponding angles can be proven equal.

Hence, this proves The Fact "If two parallel lines are cut by a transversal, each pair of corresponding angles has equal measure".

As we proved the above fact, so we can say that the converse of this above fact also hold true i.e.
"If a transversal intersect two lines such that a pair of corresponding angles is equal, then two lines are parallel to each other"