Question

in the diagram, which of the following statements are false?
∠2 and ∠6 are corresponding angles
∠1 and ∠4 are vertical angles
∠1 and ∠8 are alternate interior angles
∠4 and ∠5 are alternate interior angles

Explanation:

Step1: Recall the definition of corresponding angles

Corresponding angles are in the same relative position. $\angle2$ and $\angle6$ fit this, so this statement is true.

Step2: Recall the definition of vertical angles

Vertical angles are opposite each other. $\angle1$ and $\angle4$ are opposite, so this statement is true.

Step3: Recall the definition of alternate interior angles

Alternate interior angles are between the two lines and on opposite sides of the transversal. $\angle4$ and $\angle5$ fit this, so this statement is true.

Step4: Analyze $\angle1$ and $\angle8$

$\angle1$ and $\angle8$ are not alternate interior angles. Alternate interior angles are between the two parallel - like lines. $\angle1$ is above one of the lines and $\angle8$ is below the other, so this statement is false.

Answer:

$\angle1$ and $\angle8$ are alternate interior angles