Question

chapter 3 test
using the figure to the right, answer questions 1 and 2.

1. which three lines are parallel to \\( \overline{lm} \\)?

______ ____ ______

1. which four lines are skew to \\( \overline{lm} \\)?

______ ____ ____ ______
use the figure to the right to complete the following statements.

1. \\( \angle 1 \\) and ______ are vertical angles
2. \\( \angle 2 \\) and ______ are corresponding angles
3. \\( \angle 3 \\) and ______ are alternate interior angles
4. \\( \angle 4 \\) and ______ are alternate exterior angles
5. \\( \angle 7 \\) and ______ are consecutive interior angles
6. \\( \angle 6 \\) and ______ are a linear pair

Explanation:

Step1: Recall parallel lines definition

Parallel lines are lines in a plane that do not intersect. In the first figure, looking at the prism - like structure, lines that have the same direction as \( \overleftrightarrow{LM}\) (in terms of the 3 - D orientation of the prism) are \( \overleftrightarrow{KN}\), \( \overleftrightarrow{GJ}\), \( \overleftrightarrow{HI}\).

Step2: Recall skew lines definition

Skew lines are non - parallel and non - intersecting lines in 3 - D space. For \( \overleftrightarrow{LM}\), the lines \( \overleftrightarrow{KG}\), \( \overleftrightarrow{JH}\), \( \overleftrightarrow{NP}\), \( \overleftrightarrow{IL}\) are skew.

Step3: Recall vertical angles definition

Vertical angles are opposite angles formed by the intersection of two lines. For \( \angle1\), its vertical angle is \( \angle3\).

Step4: Recall corresponding angles definition

Corresponding angles are in the same relative position with respect to a transversal and two lines. For \( \angle2\), its corresponding angle is \( \angle6\).

Step5: Recall alternate interior angles definition

Alternate interior angles are between two lines and on opposite sides of a transversal. For \( \angle3\), its alternate interior angle is \( \angle6\).

Step6: Recall alternate exterior angles definition

Alternate exterior angles are outside two lines and on opposite sides of a transversal. For \( \angle4\), its alternate exterior angle is \( \angle5\).

Step7: Recall consecutive interior angles definition

Consecutive interior angles are between two lines and on the same side of a transversal. For \( \angle7\), its consecutive interior angle is \( \angle2\).

Step8: Recall linear pair definition

A linear pair is a pair of adjacent angles whose non - common sides are opposite rays. For \( \angle6\), its linear pair is \( \angle5\).

Answer:

1. \( \overleftrightarrow{KN}\), \( \overleftrightarrow{GJ}\), \( \overleftrightarrow{HI}\)
2. \( \overleftrightarrow{KG}\), \( \overleftrightarrow{JH}\), \( \overleftrightarrow{NP}\), \( \overleftrightarrow{IL}\)
3. \( \angle3\)
4. \( \angle6\)
5. \( \angle6\)
6. \( \angle5\)
7. \( \angle2\)
8. \( \angle5\)