Question

A transversal intersects two parallel lines, forming alternate interior angles $\angle 1$ and $\angle 2$, and vertical angles $\angle 1$ and $\angle 3$. Illustrate the situation. How are $m\angle 2$ and $m\angle 3$ related? Explain.

Short answer

The measure of angle 2 and 3 are equal, $m\angle 2=m\angle 3$.

Step-by-step solution

Step 1. Given Information.

A transversal intersects two parallel lines, forming alternate interior angles $\angle 1$ and $\angle 2$ , vertical angles $\angle 1$ and $\angle 3$.

Step 2. Definition of corresponding angles.

When two lines are crossed by another line, it is known as transversal.Corresponding angles are angles that are at the same relative position at each intersection. The measure of two corresponding angles is equal.

Step 3. Explanation.

Draw two parallel lines and a transversal on it.

The angles internal to the two parallel lines, in alternate corners of the transversal are called alternate interior angles. So, the angles $\angle 1$and $\angle 2$are located inside the two parallel lines, in alternate corners.

It is evident that $\angle 2$ and $\angle 3$ occupy the corresponding position. So, $\angle 2$ and $\angle 3$ are corresponding angles. Hence, $m\angle 2=m\angle 3$

Step 4. Conclusion.

The measure of angle 2 and 3 are equal, $m\angle 2=m\angle 3$.