Question

1. what type of lines are coplanar and do not intersect?

a parallel
b perpendicular
c segments
d transversal
for items 2 - 5, lines ( ell ) and ( m ) are intersected by transversal ( t ). ( ell parallel m )

1. select all the angles that are supplementary to ( angle 1 ).

a. ( angle 3 )
b. ( angle 4 )
c. ( angle 5 )
d. ( angle 6 )
e. ( angle 7 )
f. ( angle 8 )

1. select all the angles that are congruent to ( angle 5 ).

a. ( angle 1 )
b. ( angle 2 )
c. ( angle 3 )
d. ( angle 4 )
e. ( angle 7 )
f. ( angle 8 )

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are coplanar lines that do not intersect.

Step2: Analyze other options

• Perpendicular lines intersect at a right - angle.
• Segments are parts of lines.
• A transversal is a line that intersects two or more other lines.

Step3: For question 2

• Angles supplementary to \(\angle1\):
• \(\angle1+\angle3 = 180^{\circ}\) (linear pair).
• \(\angle1\) and \(\angle4\): Since \(\ell\parallel m\) and \(t\) is a transversal, \(\angle1\) and \(\angle4\) are not supplementary.
• \(\angle1\) and \(\angle5\): \(\angle1\) and \(\angle5\) are not supplementary.
• \(\angle1\) and \(\angle6\): \(\angle1\) and \(\angle6\) are not supplementary.
• \(\angle1\) and \(\angle7\): \(\angle1\) and \(\angle7\) are not supplementary.
• \(\angle1\) and \(\angle8\): \(\angle1\) and \(\angle8\) are not supplementary.

Step4: For question 3

• Angles congruent to \(\angle5\):
• \(\angle1\) and \(\angle5\): \(\angle1\cong\angle5\) (corresponding angles as \(\ell\parallel m\) and \(t\) is a transversal).
• \(\angle2\) and \(\angle5\): \(\angle2\) and \(\angle5\) are not congruent.
• \(\angle3\) and \(\angle5\): \(\angle3\) and \(\angle5\) are not congruent.
• \(\angle4\) and \(\angle5\): \(\angle4\) and \(\angle5\) are not congruent.
• \(\angle7\) and \(\angle5\): \(\angle7\cong\angle5\) (vertical angles).
• \(\angle8\) and \(\angle5\): \(\angle8\) and \(\angle5\) are not congruent.

Answer:

1. A. parallel
2. A. \(\angle3\)
3. A. \(\angle1\), E. \(\angle7\)