Question

Fill in the blanks :

If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are ………….

Answer 1

Co-interior angles :

As shown in the given figure, two parallel lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ and a transversal $\overleftrightarrow{PS}$ intersecting $\overleftrightarrow{AB}$ at point $Q$ and $\overleftrightarrow{CD}$ at point $R$.

$\angle AQP=\angle CRQ$ ($\because$Corresponding angles) …………………$\left(i\right)$

And, $\angle AQP=\angle AQR=180°$ ($\because$Linear pair) …………………$\left(ii\right)$

From eq. $\left(i\right)$ and $\left(ii\right)$, we get :

$\angle AQR+\angle CRQ=180°$

Similarly, $\angle BQR+\angle DRQ=180°$

$\angle AQR$, $\angle CRQ$ and $\angle BQR$, $\angle DRQ$ are the two pairs of interior angles on the same side of transversal $\overleftrightarrow{PS}$ (called co - interior angles) are supplementary.

Hence when two parallel lines are cut by a transversal then each pair of interior angles on the same side of the transversal are supplementary.