Question

State whether the given information be used to prove that two lines are parallel and also state which lines.

$\text{m}\angle \mathbf{2}=\text{m}\angle \mathbf{6}$

Short answer

The given condition can prove two lines parallel and the lines that are parallel are $\text{a}\parallel \text{b}$.

Step-by-step solution

Step 1.  Consider the diagram. 

Here, $m\angle 2=m\angle 6$.

Step 2.  Show the calculation.

Using the theorem which states-

If two lines are cut by a transversal and alternate interior angle are congruent, then lines are parallel.

Since, angle $\angle 2$ and $\angle 6$ are alternate interior angles, the line $c$ is the transversal cutting the lines $a$ and $b$, which are parallel to each other.

So, $a\parallel b$

Step 3.  State the conclusion.

Therefore, the condition $m\angle 2=m\angle 6$ proves $a\parallel b$.