Question

4.1 and 4.2 quiz
use the figure below for questions 1 - 4. (1pt each)

1. name a plane parallel to plane abc
2. name a segment parallel to \\( \overline { d e } \\).
3. name a segment parallel to \\( \overline { c f } \\).
4. name a segment skew to \\( \overline { a b } \\).

use the diagram to the right to classify each angle pair as corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, or consecutive exterior angles. (1pt each) spelling counts. no abbreviations (can use symbol for angle).

1. \\( \angle 2 \\) and \\( \angle 7 \\) ____________
2. \\( \angle 8 \\) and \\( \angle 2 \\) ____________
3. \\( \angle 3 \\) and \\( \angle 5 \\) ____________
4. \\( \angle 2 \\) and \\( \angle 6 \\) ____________
5. \\( \angle 4 \\) and \\( \angle 5 \\) ____________
6. if \\( l \parallel m \\), and \\( \angle 3 = 68 ^ { \circ } \\), find each measure. (1pt each)
7. if \\( l \parallel m \\), find the value of x. (2pts)

Explanation:

1. Name a plane parallel to Plane ABC

In a prism, opposite faces are parallel. Plane DEF is parallel to Plane ABC.

2. Name a segment parallel to \(\overline{DE}\)

Segments that do not intersect and are in parallel planes. \(\overline{AB}\) is parallel to \(\overline{DE}\)

3. Name a segment parallel to \(\overline{CF}\)

Looking at the vertical edges. \(\overline{AD}\) (or \(\overline{BE}\)) is parallel to \(\overline{CF}\)

4. Name a segment skew to \(\overline{AB}\)

Skew lines are non - parallel and non - intersecting. \(\overline{CF}\) (or \(\overline{DE}\), \(\overline{DF}\), \(\overline{EF}\)) is skew to \(\overline{AB}\)

5. \(\angle2\) and \(\angle7\)

Alternate exterior angles (they are on the outside of the two lines and on opposite sides of the transversal)

6. \(\angle8\) and \(\angle2\)

Alternate interior angles (they are on the inside of the two lines and on opposite sides of the transversal)

7. \(\angle3\) and \(\angle5\)

Consecutive interior angles (they are on the inside of the two lines and on the same side of the transversal)

8. \(\angle2\) and \(\angle6\)

Corresponding angles (they are in the same relative position)

9. \(\angle4\) and \(\angle5\)

Consecutive exterior angles (they are on the outside of the two lines and on the same side of the transversal)

10. If \(l\parallel m\), and \(\angle3 = 68^{\circ}\)

• \(a. m\angle1\): \(\angle1\) and \(\angle3\) are vertical angles. \(m\angle1 = 68^{\circ}\)
• \(b. m\angle2\): \(\angle2\) and \(\angle3\) are supplementary. \(m\angle2=180 - 68=112^{\circ}\)
• \(c. m\angle3 = 68^{\circ}\) (given)
• \(d. m\angle4\): \(\angle4\) and \(\angle3\) are supplementary. \(m\angle4 = 112^{\circ}\)
• \(e. m\angle5\): \(\angle5\) and \(\angle3\) are alternate interior angles. \(m\angle5 = 68^{\circ}\)
• \(f. m\angle6\): \(\angle6\) and \(\angle2\) are alternate interior angles. \(m\angle6 = 112^{\circ}\)
• \(g. m\angle7\): \(\angle7\) and \(\angle3\) are corresponding angles. \(m\angle7 = 68^{\circ}\)
• \(h. m\angle8\): \(\angle8\) and \(\angle4\) are corresponding angles. \(m\angle8 = 112^{\circ}\)

11. If \(l\parallel m\)

\((9x - 4)+(5x + 16)=180\) (consecutive interior angles are supplementary)
\(9x-4 + 5x+16=180\)
\(14x+12 = 180\)
\(14x=180 - 12\)
\(14x=168\)
\(x = 12\)

Answer:

1. Plane DEF
2. \(\overline{AB}\)
3. \(\overline{AD}\) (or \(\overline{BE}\))
4. \(\overline{CF}\) (or \(\overline{DE}\), \(\overline{DF}\), \(\overline{EF}\))
5. Alternate exterior angles
6. Alternate interior angles
7. Consecutive interior angles
8. Corresponding angles
9. Consecutive exterior angles

10.

• a. \(68^{\circ}\)
• b. \(112^{\circ}\)
• c. \(68^{\circ}\)
• d. \(112^{\circ}\)
• e. \(68^{\circ}\)
• f. \(112^{\circ}\)
• g. \(68^{\circ}\)
• h. \(112^{\circ}\)

1. \(x = 12\)