Question

drag the lines to the boxes to form correct pairs.

in the diagram, transversal ( f ) cuts across the parallel lines ( a ) and ( b ). match the pairs of angles with the relationship that shows they are congruent.

alternate exterior angles ( angle 2, angle 7 ) and ( angle 5, angle 8 ) alternate interior angles
( angle 1, angle 8 ) and ( angle 2, angle 7 ) corresponding angles ( angle 3, angle 6 ) and ( angle 4, angle 5 )
vertical angles ( angle 1, angle 5 ) and ( angle 2, angle 6 )

Explanation:

Step1: Recall the definitions

Alternate exterior angles: Angles that lie outside the two parallel lines and on opposite sides of the transversal.
Alternate interior angles: Angles that lie between the two parallel lines and on opposite sides of the transversal.
Corresponding angles: Angles that are in the same relative position with respect to the parallel lines and the transversal.
Vertical angles: Angles that are opposite each other when two lines intersect.

Step2: Match the angle - pair and the relationship

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

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 $\angle5,\angle8$