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Theorem 3 – Pair of Consecutive Interior Angles are Supplementary

Theorem 3
If a transversal intersects two parallel lines, each pair of consecutive interior angles is supplementary.


Given: Transversal intersects two parallel lines AB and CD at M and N respectively, making two pairs of consecutive interior angles, 4, 5 and 3, 6.

To Prove: 5 + 4 = 180° and 6 + 3 = 180°
 


Proof: Since ray ME stands on line AB
1 + 2 = 180° …. (Linear Pair)
Also
2 = 6 …. (Corresponding angles)
1 + 6 = 180°
1 = 3 …. (Vertically opposite angles)

3 + 6 = 180°

Again, ray NE stands on CD
4 + 3 = 180° …. (Linear pair)
But
3 = 5
Hence
5 + 4 = 180°.

 





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