Loading....
Coupon Accepted Successfully!

 

Theorem 5 – Converse of Pair of Consecutive Interior Angles are Supplementary

Theorem 5
If a transversal intersects two lines in such a way that a pair of consecutive interior angles are supplementary, the two lines are parallel.

Given: A transversal EF intersects two lines AB and CD at M and N respectively such that 3 and 6 is a pair of consecutive interior angles, and 3 + 6 = 180°.

To Prove: AB | | CD


Proof: Since ray FM stands on line AB
3  + 4 = 180° …(Linear pair)
We are given
3 + 6 = 180°
4 + 3 = 3 + 6
4 = 6
Since
4 and 6 are Alternate angles and are equal
AB | | CD … (Corresponding angles axiom)
.





Test Your Skills Now!
Take a Quiz now
Reviewer Name