. If a transversal intersects two parallel lines


 then each pair of interior angles are supplementary". Prove it.

Best Answer

Explanation:

Let the situation be represented by a diagram.

supplementary

 

To prove ∠1+∠3 =180º ,∠2+∠4 =180º

Now, by linear pair of angles,

∠3+∠5 =180º

But ∠1 =∠5 as they are corresponding angles.

So, 

∠1+∠3 =180º

Now, by linear pair,

∠6+∠2 =180º

But ∠4 =∠6 as they are corresponding angles.

So, 

∠2+∠4 =180º

Hence, proved.

Final Answer:

 If a transversal intersects two parallel lines, then each pair of interior angles are supplementary.

 

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