Section 1: Parallel Lines and Transversals
Vocabulary: Parallel and Skew
Parallel Lines: Coplanar lines that do not intersect
Skew Lines: two lines that do not intersect and are not parallel
Parallel Planes: Planes that do not intersect
Example:
Identify each of the following using the cube shown.
Identify each of the following using the cube shown.
A.. Name all segments Parallel to BC.
AD, EH, FG
B. Name all Segments skew to EH.
AB, CD, BG, or CF
C. Name a plane parallel to ABG
Plane CDE
Vocabulary: Transversal Angle Pair Relationships
Transversal: A line that intersects two or more coplanar lines
at two different points
Interior Angles: Angles that lie between two transversals that intersect the same line
Exterior Angles: Angles that lie outside of the transversal, this is the contrast of the interior angle
Consecutive Interior Angles: When two lines are crossed by the transversal, the pairs of angles on one side of the transversal but inside the two lines are consecutive
Alternate Interior Angles: When two lines are crossed by the transversal, the pairs of angles on opposite sides of the transversal but inside the two lines are called alternate interior
Alternate Exterior Angles: When two lines are crossed by the transversal, the pairs of angles on opposite sides of the transversal but outside the two lines are called alternate exterior
Corresponding Angles: When two lines are crossed by the transversal, the angles in matching corners are corresponding
Example:
Refer to the figure below, classify the relationship between each pair of angles
Refer to the figure below, classify the relationship between each pair of angles
A. Classify the relationship between <2 and <6
These angles are considered corresponding because the two lines are crossed by a transversal and angles <2 and <6 are in the corresponding matching corners
B. Classify the relationship between <1 and <7
These angles are considered alternate exterior because they are on the opposite sides of the transversal, however they are outside of
the two lines
C. Classify the relationship between <3 and <8
These angles are considered consecutive interior because they lie
outside of the transversal and inside of the two lines
These angles are considered corresponding because the two lines are crossed by a transversal and angles <2 and <6 are in the corresponding matching corners
B. Classify the relationship between <1 and <7
These angles are considered alternate exterior because they are on the opposite sides of the transversal, however they are outside of
the two lines
C. Classify the relationship between <3 and <8
These angles are considered consecutive interior because they lie
outside of the transversal and inside of the two lines
Real-world Example:
In this real world photograph, lines M and N are not parallel and will eventually intersect. However line P is the transversal because it intersects both lines
Try it out: Based on the image below, answer the following questions.
1. Classify the relationship between <4 and <5
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
2. Classify the relationship between <7 and <9
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
3. Classify the relationship between <4 and <7
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
2. Classify the relationship between <7 and <9
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
3. Classify the relationship between <4 and <7
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior
Answers:
1. The answer is D. They are consecutive interiors since they are on one side of the transversal, but in between the two lines
2. The answer is C. They are corresponding angles because angles <7 and <9 in the matching corners correspond to each other
3. The answer is B. They are alternate exterior angles beacuse they are on opposite sides of the transversal, but outside of the two lines
2. The answer is C. They are corresponding angles because angles <7 and <9 in the matching corners correspond to each other
3. The answer is B. They are alternate exterior angles beacuse they are on opposite sides of the transversal, but outside of the two lines