Question

1. in the diagram below, lines a and b are parallel and intersected by transversal t.

use the diagram and answer choices below to complete each sentence.

a. angles 1 and 5 are _______. e
b. angles 2 and 8 are _______. a
c. angles 3 and 6 are _______. d
d. angles 4 and 6 are _______. b
e. angles 6 and 8 are _______. g
f. angles 3 and 4 are _______. f
g. angles 2 and 7 are _______. c

answer choices:
a. alternate exterior angles
b. alternate interior angles
c. consecutive exterior angles
d. consecutive interior angles
e. corresponding angles
f. linear pair
g. vertical angles

Explanation:

Part a

Step1: Recall Corresponding Angles

Corresponding angles are in the same position relative to the parallel lines and transversal. Angles 1 and 5 are in the same relative position (both below the parallel lines and to the left of the transversal? Wait, no, angle 1 is at the intersection of a and t, angle 5 at b and t. Wait, actually, corresponding angles are when two parallel lines are cut by a transversal, the angles that occupy the same relative position at each intersection. So angle 1 (on line a, below transversal t) and angle 5 (on line b, below transversal t, same side? Wait, no, maybe I got the diagram wrong. Wait, the answer choice is E. Corresponding Angles. So angles 1 and 5 are corresponding angles.

Step2: Match with Answer Choice

Step1: Recall Alternate Exterior Angles

Alternate exterior angles are on opposite sides of the transversal and outside the two parallel lines. Angle 2 is on line a, above transversal t (exterior? Wait, line a and b are parallel, transversal t. Angle 2 is above line a, angle 8 is below line b. Wait, alternate exterior angles: angle 2 (exterior to the space between a and b) and angle 8 (exterior to the space between a and b), on opposite sides of transversal t. So alternate exterior angles. Answer choice A is Alternate exterior angles.

Step2: Match with Answer Choice

Step1: Recall Consecutive Interior Angles

Consecutive interior angles are on the same side of the transversal and inside the two parallel lines. Angle 3 is on line a, above transversal t (inside the space between a and b? Wait, line a and b are parallel, transversal t. Angle 3 is between a and t, angle 6 is between b and t, same side of transversal? Wait, consecutive interior angles are also called same - side interior angles. So angle 3 and 6: are they on the same side of transversal t and inside the two parallel lines? Let's see, angle 3 is on line a, above t, angle 6 is on line b, above t? Wait, no, maybe I messed up. Wait, answer choice D is Consecutive interior angles. So angle 3 and 6 are consecutive interior angles.

Step2: Match with Answer Choice

Answer:

choice E is Corresponding Angles, so that's the match.