Question

name:
date:
topic:
class:
main ideas/questions
notes/examples
parallel
lines
•____ lines that never ____
•______ are used to indicate the lines are parallel.
•symbolic notation:______
parallel
planes
•____ that never ____.
•symbolic notation:______
skew
lines
•____ lines that never ____
•examples:____ & ____
____ & ____
____ & ____
example 1
a. name all segments parallel to \\( \overline { a e } \\).______
b. give two examples of parallel planes.
(1)____ & ____
(2)____ & ____
c. name all segments skew to \\( \overline { g h } \\).______
example 2
a. name all segments parallel to \\( \overline { j k } \\).______
b. name all segments parallel to \\( \overline { n s } \\).______
c. name a plane parallel to plane \\( j k l \\).______
d. name four segments skew to \\( \overline { r q } \\).______

Explanation:

PARALLEL LINES

Step1: Definition

Parallel lines are coplanar lines that never intersect.

Step2: Indication

Arrowheads are used to indicate the lines are parallel.

Step3: Symbolic Notation

If we have two lines \(AB\) and \(CD\), the symbolic notation is \(AB\parallel CD\).

PARALLEL PLANES

Step1: Definition

Parallel planes are planes that never intersect.

Step2: Symbolic Notation

If we have two planes \(J\) and \(K\), the symbolic notation is \(J\parallel K\).

SKEW LINES

Step1: Definition

Skew lines are non - coplanar lines that never intersect.

Step2: Examples (using the cube in the skew lines section)

For example, in a cube, \(TW\) & \(UR\), \(TW\) & \(QR\), \(TW\) & \(SR\) (assuming the cube has vertices labeled as in a standard rectangular prism).

EXAMPLE 1

a. Name all segments parallel to \(\overline{AE}\)

In a rectangular prism (the figure for example 1), segments parallel to \(\overline{AE}\) are \(\overline{BF}\), \(\overline{CG}\), \(\overline{DH}\).

b. Give two examples of parallel planes

(1) Plane \(AEHD\) & Plane \(BFGC\) (2) Plane \(ABFE\) & Plane \(DCGH\)

c. Name all segments skew to \(\overline{GH}\)

Segments skew to \(\overline{GH}\) are \(\overline{AB}\), \(\overline{BC}\), \(\overline{CD}\), \(\overline{DA}\), \(\overline{AE}\), \(\overline{BF}\)

EXAMPLE 2

a. Name all segments parallel to \(\overline{JK}\)

Assuming the figure is a prism, segments parallel to \(\overline{JK}\) are \(\overline{ML}\), \(\overline{ON}\), \(\overline{RQ}\)

b. Name all segments parallel to \(\overline{NS}\)

Segments parallel to \(\overline{NS}\) are \(\overline{MP}\), \(\overline{OQ}\), \(\overline{LR}\)

c. Name a plane parallel to plane \(JKL\)

A plane parallel to plane \(JKL\) is plane \(MNO\)

d. Name four segments skew to \(\overline{RQ}\)

Four segments skew to \(\overline{RQ}\) are \(\overline{JK}\), \(\overline{ML}\), \(\overline{ON}\), \(\overline{LP}\)

Answer:

PARALLEL LINES

• Coplanar, intersect, Arrowheads, \(AB\parallel CD\)

PARALLEL PLANES

• Planes, intersect, \(J\parallel K\)

SKEW LINES

• Non - coplanar, intersect, \(TW\) & \(UR\), \(TW\) & \(QR\), \(TW\) & \(SR\)

EXAMPLE 1

• a. \(\overline{BF}\), \(\overline{CG}\), \(\overline{DH}\)
• b. (1) Plane \(AEHD\) & Plane \(BFGC\) (2) Plane \(ABFE\) & Plane \(DCGH\)
• c. \(\overline{AB}\), \(\overline{BC}\), \(\overline{CD}\), \(\overline{DA}\), \(\overline{AE}\), \(\overline{BF}\)

EXAMPLE 2

• a. \(\overline{ML}\), \(\overline{ON}\), \(\overline{RQ}\)
• b. \(\overline{MP}\), \(\overline{OQ}\), \(\overline{LR}\)
• c. Plane \(MNO\)
• d. \(\overline{JK}\), \(\overline{ML}\), \(\overline{ON}\), \(\overline{LP}\)