Title of Lesson: Parallel and Perpendicular Lines in Real World
Subject: Geometry
Grade level: 10th
Teacher: Mrs. Christina Leonard
Objective(s):
The students will be able to correctly identify parallels and perpendiculars in the real world in terms of both
lines and planes.
SCSDE Curriculum Standard(s) Addressed:
Standard G-1: The student will understand and utilize the mathematical processes of problem solving,
reasoning and proof, communication, connections, and representation.
G-1.4 Formulate and test conjectures by using a variety of tools such as concrete models, graphing calculators,
spreadsheets, and dynamic geometry software.
G-1.9 Demonstrate an understanding of how geometry applies to in real-world contexts (including architecture,
construction, farming, and astronomy).
Standard G-7: The student will demonstrate through the mathematical processes an understanding of the
surface area and volume of the three-dimensional objects.
G-7.4 Apply congruence and similarity relationships among geometric objects to solve problems.
NCTM National Curriculum Standard(s) Addressed:
Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop
mathematical arguments about geometric relationships: explore relationships (including congruence
and similarity) among classes of two- and three-dimensional geometric objects, make and test
conjectures about them, and solve problems involving them
Use visualization, spatial reasoning, and geometric modeling to solve problems: visualize three-dimensional
objects and spaces from different perspectives and analyze their cross sections
Prerequisites:
The students must be able to construct parallel lines and understand the characteristics before addressing
this topic (distance between two parallel lines always equal, same slope same intercept is the same line, parallel
lines are in the same plane with the same slope).
Materials/Preparation:
Pictorial interpretations, 3-dimensional interpretations
Procedures: 
Introductory Activity:
As an entire class review the definition and characteristics of parallel by asking the class for each and
listening for responses as well as clarifying which is/are correct. Have the students consider how this can be
applied on a 3-dimensional level as well. Have the students come up of a list of examples of parallels and
perpendiculars in three-dimension on their own.
Main Activity:
First display 2-dimensional examples of parallel and perpendicular lines on a coordinate plane. Use techniques
to prove that the lines are parallel (same slope) and perpendicular (slopes are inverse reciprocals). Give the
definition of skew lines. Skew lines: lines that do not intersect and are not parallel. Using a cube drawing, ask
the students to show an example of skew lines. Have the students consider the opening activity and
incorporate skew lines into their original three-dimension shapes. Using the cube drawing, have the students
provide lines that are parallel and perpendicular. Ask the class if anyone considered using planes as opposed to
lines. Introduce the idea that even planes could be parallel or perpendicular. Using two pieces of paper show
interpretations of parallel planes showing that there is no intersection between parallel planes. Cutting a
straight line in one of the pieces of paper slide the other through the cut, this will act as an interpretation of
two perpendicular planes. Ask the students what type of intersection is created between two parallel planes
(none.) Ask the students what type of intersection is created between two perpendicular planes (a line.) Use
the pieces of paper to show the line intersection of the two perpendicular planes. Have the students share
their examples from the opening activity if they think they are still correct. After exploring multiple answers,
have them share responses that they now think are correct. Ask the students how their conjectures changed
from the beginning of class to the end. What made them change their minds? What would you consider about a
line being perpendicular to a plane and the intersection between the two?
Closure: At the end of the lesson main points will be brought up again to ensure that the class not only
understands the main points but that they are aware what parts of the lesson are the most important:
-So what are skew lines?
-Therefore, parallel lines have to be in the same? Plane.
-What is the intersection of parallel lines? Parallel planes? Perpendicular lines? Perpendicular planes?
-What would the intersection of a line and a plane be?
-What would the intersection of a plane and a sphere be? A plane and a cone? A plane and a rectangular
pyramid?
Assessment: Assessment will be accomplished by responses during the lesson to discover the level of
classroom understanding, and practice problems will be completed after the lesson.
1. Using the numbered vertices, find sets of parallel lines, perpendicular lines, parallel planes, perpendicular
planes.
2. Name objects in the real-world that have parallels and perpendiculars. Explain the parallels and
perpendiculars in these objects and whether they are lines or planes.
Adaptations:
In this lesson the students are allowed to think on their own level and stretch their minds to their own levels
of ability by being given such a vague description of what to look for. This allows all levels of mathematical
understanding to reach their maximum levels of thinking.
Follow-up Lessons/Activities:
A follow-up lesson would be considering other 3-dimensional shapes that are less able to visualize and may have
to be broken down into different shapes to consider and prove that the different aspects are parallel and
perpendicular.