Checking for Parallel Lines

When two coplanar lines are cut by a transversal, which condition does not guarantee that the two lines are parallel.

For the figure $\angle a=\angle b=55°$, find the relation between $AB$ and $CD$

In the given figure, find the relation between $x$ and $y$.

For the figure $\angle b=\angle d=35°$, then $PQ$ is _____ to $XY$.

Find the relation of the lines $AB$ and $CD$ when $\angle a=\angle c$

Given that $\angle \mathrm{AEC}=50°$ ,$\mathrm{AB} = \mathrm{BC}, \mathrm{AOE}$ is the diameter, find $\angle \mathrm{AOB}$. Hence, show that $\mathrm{BO}\left|\right|\mathrm{CE}$.

$\mathrm{P}$ is the midpoint of an arc $\mathrm{APB}$ of a circle. Prove that the tangent drawn at $\mathrm{P}$ will be parallel to the chord $\mathrm{AB}.$

In a cyclic quadrilateral $\mathrm{ABCD},$ the diagonal $\mathrm{AC}$ bisects the angle $\mathrm{BCD}.$ Prove that the diagonal $\mathrm{BD}$ is parallel to the tangent to the circle at point $\mathrm{A}.$

Study the figure shown here (not drawn to scale), If $ABG$ is a straight line, then find $\angle ABH$ and reflex $\angle ABC$ respectively.