Question

e diagram, transversal t cuts across the parallel lines a and b. match the pairs of angles with the relationship that shows they are congruent. alternate exterior angles ∠2, ∠3 and ∠5, ∠8 alternate interior angles ∠1, ∠8 and ∠2, ∠7 corresponding angles ∠3, ∠6 and ∠4, ∠5 vertical angles ∠1, ∠5 and ∠2, ∠6 d.

Explanation:

• Alternate exterior angles: Angles that lie outside the two parallel lines and on opposite sides of the transversal. So, $\angle1,\angle8$ and $\angle2,\angle7$ are alternate exterior angles.
• Alternate interior angles: Angles that lie between the two parallel lines and on opposite sides of the transversal. So, $\angle3,\angle6$ and $\angle4,\angle5$ are alternate interior angles.
• Corresponding angles: Angles that are in the same relative position with respect to the parallel lines and the transversal. So, $\angle1,\angle5$ and $\angle2,\angle6$ are corresponding angles.
• Vertical angles: Angles that are opposite each other when two lines intersect. So, $\angle2,\angle3$ and $\angle5,\angle8$ are vertical angles.

Answer:

• alternate exterior angles $\longleftrightarrow\angle1,\angle8$ and $\angle2,\angle7$
• alternate interior angles $\longleftrightarrow\angle3,\angle6$ and $\angle4,\angle5$
• corresponding angles $\longleftrightarrow\angle1,\angle5$ and $\angle2,\angle6$
• vertical angles $\longleftrightarrow\angle2,\angle3$ and $\angle5,\angle8$