Question

1. use the diagram below to answer the following questions.

a) name a transversal.
b) name all corresponding angles.
c) name all alternate interior angles.
d) name all alternate exterior angles.
e) name all consecutive interior angles.
f) name all consecutive exterior angles.

1. use the diagram below to answer the following questions

Explanation:

Step1: Recall Transversal Definition

A transversal is a line that intersects two or more other lines. In the diagram, line \( i \) intersects lines \( l \) and \( k \), so \( i \) is a transversal.

Step2: Corresponding Angles

Corresponding angles are in the same position relative to the transversal and the two lines. So \( \angle 1 \) and \( \angle 3 \), \( \angle 5 \) and \( \angle 7 \), \( \angle 2 \) and \( \angle 4 \), \( \angle 6 \) and \( \angle 8 \).

Step3: Alternate Interior Angles

Alternate interior angles are between the two lines and on opposite sides of the transversal. So \( \angle 2 \) and \( \angle 7 \), \( \angle 3 \) and \( \angle 6 \).

Step4: Alternate Exterior Angles

Alternate exterior angles are outside the two lines and on opposite sides of the transversal. So \( \angle 1 \) and \( \angle 8 \), \( \angle 4 \) and \( \angle 5 \).

Step5: Consecutive Interior Angles

Consecutive interior angles are between the two lines and on the same side of the transversal. So \( \angle 2 \) and \( \angle 3 \), \( \angle 6 \) and \( \angle 7 \).

Step6: Consecutive Exterior Angles

Consecutive exterior angles are outside the two lines and on the same side of the transversal. So \( \angle 1 \) and \( \angle 5 \), \( \angle 4 \) and \( \angle 8 \).

Answer:

s:
a) Transversal: Line \( i \)
b) Corresponding angles: \( \angle 1 \) and \( \angle 3 \), \( \angle 5 \) and \( \angle 7 \), \( \angle 2 \) and \( \angle 4 \), \( \angle 6 \) and \( \angle 8 \)
c) Alternate interior angles: \( \angle 2 \) and \( \angle 7 \), \( \angle 3 \) and \( \angle 6 \)
d) Alternate exterior angles: \( \angle 1 \) and \( \angle 8 \), \( \angle 4 \) and \( \angle 5 \)
e) Consecutive interior angles: \( \angle 2 \) and \( \angle 3 \), \( \angle 6 \) and \( \angle 7 \)
f) Consecutive exterior angles: \( \angle 1 \) and \( \angle 5 \), \( \angle 4 \) and \( \angle 8 \)