Question

Which criteria will prove line $p||q$

• A. $x=y$
• B. $z=x$
• C. $y=z$
• D. $x+y={180}^o$

Answer 1

Answer: (C), (D)

$x+y={180}^o$

We know that if the sum of co-interior angles of two lines, which are intersected by a transversal, equals to ${180}^o$ then two lines are parallel by co interior angle theorem.

If two lines are intersected by third line and the alternate interior angles so formed are equal, then also the two lines are parallel to each other by alternate interior angle theorem.

As, in the figure we know that, $z$ and $y$ are alternate interior angles.
$x$ and $y$ are Co-interior angles.
so option $\left(c\right)$ and $\left(d\right)$ are correct.