Question

example: classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a. ∠10 and ∠16 b. ∠4 and ∠12 c. ∠12 and ∠13 d. ∠3 and ∠9 practice use the figure in the example for practice a - l. identify the transversal connecting each pair of angles. a. ∠9 and ∠13 b. ∠5 and ∠14 c. ∠4 and ∠6 classify the relationship between each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. d. ∠1 and ∠5 e. ∠6 and ∠14 f. ∠2 and ∠8 g. ∠3 and ∠11 h. ∠12 and ∠3 i. ∠4 and ∠6 j. ∠6 and ∠16 k. ∠11 and ∠14 l. ∠10 and ∠16

Explanation:

Step1: Recall angle - relationship definitions

Alternate interior angles are non - adjacent angles between two parallel lines and on opposite sides of a transversal. Alternate exterior angles are non - adjacent angles outside two parallel lines and on opposite sides of a transversal. Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. Consecutive interior angles are between two parallel lines and on the same side of a transversal.

Step2: Analyze each pair of angles in the figure

a. For ∠9 and ∠13

The transversal is the line that intersects the two lines containing the angles. Here, the transversal is the vertical line on the right - hand side of the figure. They are corresponding angles as they are in the same relative position with respect to the parallel lines and the transversal.

b. For ∠5 and ∠14

The transversal is the horizontal line at the bottom of the figure. They are non - related in the given angle - relationship types.

c. For ∠4 and ∠6

The transversal is the left - hand side vertical line. They are consecutive interior angles as they are between the parallel lines and on the same side of the transversal.

d. For ∠1 and ∠5

The transversal is the left - hand side vertical line. They are corresponding angles as they are in the same relative position with respect to the parallel lines and the transversal.

e. For ∠6 and ∠14

The transversal is the bottom horizontal line. They are alternate interior angles as they are between the parallel lines and on opposite sides of the transversal.

f. For ∠2 and ∠8

The transversal is the left - hand side vertical line. They are corresponding angles as they are in the same relative position with respect to the parallel lines and the transversal.

g. For ∠3 and ∠11

The transversal is the right - hand side vertical line. They are alternate exterior angles as they are outside the parallel lines and on opposite sides of the transversal.

h. For ∠12 and ∠3

The transversal is the right - hand side vertical line. They are non - related in the given angle - relationship types.

i. For ∠4 and ∠6

The transversal is the left - hand side vertical line. They are consecutive interior angles as they are between the parallel lines and on the same side of the transversal.

j. For ∠6 and ∠16

The transversal is the bottom horizontal line. They are non - related in the given angle - relationship types.

k. For ∠11 and ∠14

The transversal is the right - hand side vertical line. They are non - related in the given angle - relationship types.

l. For ∠10 and ∠16

The transversal is the right - hand side vertical line. They are corresponding angles as they are in the same relative position with respect to the parallel lines and the transversal.

Answer:

a. Corresponding angles
b. No specific relationship
c. Consecutive interior angles
d. Corresponding angles
e. Alternate interior angles
f. Corresponding angles
g. Alternate exterior angles
h. No specific relationship
i. Consecutive interior angles
j. No specific relationship
k. No specific relationship
l. Corresponding angles