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NM Standards: GT-A-7

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**Parallel Lines Coplanar lines that do not intersect.**

The symbol || means “is parallel to” The red arrows also mean “is parallel to”

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Parallel Planes Two or more planes that do not intersect. R Q

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**Skew lines are always on different planes.**

Two or more lines that do not intersect but are not parallel. Lines m & n are skew lines n m Skew lines are always on different planes.

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**Name all planes that are parallel to plane AEF.**

Answer: plane BHG Example 1-1a

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**Name all segments that intersect**

Answer: Example 1-1b

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**Name all segments that are parallel to**

Answer: Example 1-1c

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**Name all segments that are skew to**

Answer: Example 1-1d

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Example 1-1e

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Transversal A line that intersects two or more other lines in a plane at different points The two or more lines do NOT have to be parallel.

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**BUS STATION Some of a bus station’s driveways are shown**

BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal. Answer: If the lines are extended, line v intersects lines u, w, x, and z. Example 1-2a

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**BUS STATION Some of a bus station’s driveways are shown**

BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal. Answer: lines u, w, x, z Example 1-2b

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**BUS STATION Some of a bus station’s driveways are shown**

BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal. Answer: lines v, x, y, z Example 1-2c

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**BUS STATION Some of a bus station’s driveways are shown**

BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line w is a transversal. Answer: lines v, x, y, z Example 1-2d

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**HIKING A group of nature trails is shown**

HIKING A group of nature trails is shown. Identify the sets of lines to which each given line is a transversal. a. line a b. line b c. line c d. line d Answer: lines c, d, e, f Answer: lines c, d, e, f Answer: lines a, b, d, e, f Answer: lines a, b, c, e, f Example 1-2e

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Types of Angles Exterior Angles: Angles that lie outside the lines cut by a transversal Interior Angles: Angles that lie between the lines cut by a transversal Consecutive Interior Angles: Pairs of interior angles formed by a transversal that lie on the same side of the transversal and share a side. Alternate Exterior Angles: Pairs of exterior angles formed by a transversal that lie on opposite sides of the transversal. Alternate Interior Angles: Pairs of interior angles formed by a transversal that lie on opposite sides of the transversal. Corresponding Angles: Pairs of angles formed by a transversal that lie on the same side of the transversal, but one is interior and one is exterior.

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Key Concepts

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**Answer: corresponding**

Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Example 1-3a

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**Answer: alternate exterior**

Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior Example 1-3b

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**Answer: corresponding**

Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Example 1-3c

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**Answer: alternate exterior**

Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior Example 1-3d

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**Answer: alternate interior**

Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior Example 1-3e

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**Answer: consecutive interior**

Identify as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior Example 1-3f

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Example 1-3g

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4.5 Introduction to Parallel Lines

4.5 Introduction to Parallel Lines

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