Properties of Parallel Lines and their Transversal

In diagram, the sides of $\angle PQR$ and $\angle XYZ$ are parallel to each other. Prove that, $\angle PQR\cong \angle XYZ$.

In the given diagram, $PQ$ and $RS$ are two mirrors placed parallel to each other. An incident ray $AB$ strikes the mirror $PQ$ at $B,$ the reflected ray moves along the path $BC$ and strikes the mirror $RS$ at $C$ and again reflects back along $CD.$ Prove that $AB\parallel CD.$

In the given diagram, $AB\parallel CD$ and $BC\parallel ED$. Then find the value of $x$.

In the given diagram, $AB\parallel CD$. Prove that$p+q-\mathrm{r}=180$

In the figure, $l_1\parallel l_2$, $l_2\parallel l_3$ and $m_1\parallel m_2$.  If $\angle 1=115°$, then $\angle 2=k°$, find $k$.

Two lines are intersected by a transversal then $b=$_____$°$.

What is the size of the angle marked $x$ in this figure?

In the diagram below, $p\parallel q$ and $q\parallel r$. Find $\mathrm{m}\angle 8$.

The flag of the United States has $13$ alternating red and white stripes. Each stripe is parallel to the stripe immediately below it. Explain why the top stripe is parallel to the bottom stripe.

In the figure, $l_1\parallel l_2$, $l_2\parallel l_3$ and $m_1\parallel m_2$.  If $\angle 1=115°$, then $\angle 2=k°$, find $k$.

In the given figure $l\parallel m, t\perp m \text{and} t\perp n$ then is $l\parallel n$? Why?

 Determine if the lines p, q, and r are parallel.

If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.

$\mathrm{m}\angle 3+\mathrm{m}\angle 6=180°$, prove that $\mathrm{AB}\parallel \mathrm{CD}$.

$\mathrm{m}\angle 5+\mathrm{m}\angle 4=180°$, prove that $\mathrm{AB}\parallel \mathrm{CD}$.

Are the following lines $\mathrm{p}$ and $\mathrm{q}$ parallel?

Are the following lines $\mathrm{l}$ and $\mathrm{m}$ parallel?

In the given figure, $\mathrm{BAD}\parallel \mathrm{EF}, \angle \mathrm{AEF}=55°$ and $\angle \mathrm{ACB}=25°$. If $\angle \mathrm{ABC}=\mathrm{k}°$, then find the value of $\mathrm{k}$.

In the given figure, $\mathrm{BAD}\parallel \mathrm{EF}, \angle \mathrm{AEF}=55°$ and $\angle \mathrm{ACB}=25°$. If $\angle \mathrm{ABC}=\mathrm{k}°$, then find the value of $\mathrm{k}$.

In the given figure $\mathrm{AB}\parallel \mathrm{CD}; \mathrm{BC}\parallel \mathrm{DE}$ then find the values of $x$ and $y$.