Download Title of Lesson: Introducing Lines Cut By a Transversal Subject

Title of Lesson: Introducing Lines Cut By a Transversal
Subject: Geometry
Grade level: 10th
Teacher: Mrs. Christina Leonard
Objective(s):
The students will be able to explore the special angles in a pair of parallel lines cut by a transversal. The
students will be able to solve for angles when one is given when a pair of parallel lines are cut by a transversal
and one angle is given. Each student will be able to understand the difference between parallel lines cut by a
transversal and non-parallel lines cut by a transversal.
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-1.1 Demonstrate an understanding of the axiomatic structure of geometry by using undefined terms,
definitions, postulates, theorems, and corollaries.
G-1.2 Communicate knowledge of geometric relationships by using mathematical terminology appropriately.
Standard G-2: The student will demonstrate through the mathematical processes an understanding of the
properties of basic geometric figures and the relationships between and among them.
G-2.2 Apply properties of parallel lines, intersecting lines, and parallel lines cut by a transversal to solve
problems.
Standard G-6: The student will demonstrate through the mathematical processes an understanding of
transformations, coordinate geometry, and vectors.
G-6.3 Apply transformations—translation, reflection, rotation, and dilation—to figures in the coordinate plane
by using sketches and coordinates.
NCTM National Curriculum Standard(s) Addressed:
Use visualization, spatial reasoning, and geometric modeling to solve problems: draw and construct
representations of two- and three-dimensional geometric objects using a variety of tools
Specify locations and describe spatial relationships using coordinate geometry and other representational
systems: use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical
systems, to analyze geometric situations
Prerequisites: When first being addressed with the lesson the students must be able to understand
supplementary angles and parallel lines.
Materials/Preparation: Google sketch up and Geogebra
Procedures: 
Introductory Activity: In the beginning of class, old material that leads into the lesson is reviewed.
Supplementary angles are discussed in terms of giving one angle and finding the missing angle. Parallel lines are
reviewed by considering same direction and same slope continuously throughout and that the distance between
two parallel lines is always equal.
Main Activity: The main activity begins with google sketch up. In google sketch up two tall buildings are
already constructed with a window on the top of one building as well as a window on the bottom of the other
both facing each other. A line is connected from the inside of one building to the inside of the other through
the windows. The students are addressed with the situation “consider that one adventurous person decides to
create a zip line from the top floor of one building into the bottom floor of the next.” Then questions are
asked such as what do you think about the angle the person leaves the building compared to the entrance of
the second, if they were to break all the way through out of the other end how would this angle compare, and
how do you think we can set up this problem to solve for the comparison in the different angle measurements.
This situation will also be interpreted in a different aspect. Simply drawn on the board the students will be
asked how the situation can be presented on the board through a simple drawing. This gets the students
engaged since the situation is more exciting, as well as activating prior knowledge of angles corresponding.
Next, when the situation is represented only by two lines cut by a transversal, explore the different special
angles in the diagram. Discuss what the terms exterior and interior mean in aspects of two parallel lines by
splitting into an interior area and an exterior area as a whole class. Have the class determine the interior
angles and exterior angles of the diagram.
Then discuss what alternate and corresponding mean in a sense off opposite or same side that can be related
to special angles names later. Have them conjecture what two angles could possibly create consecutive interior
angles, alternate exterior angles, alternate interior angles, and corresponding angles exploring each special
angle category individually. Begin with just focusing on interior angles, from there the angle pairs they can
create are either on the same side of the transversal (consecutive) or opposite one another on the transversal
(alternate). When we are just exploring exterior angles, the only special angle pair we will be dealing with will
be opposite one another on the transversal. Corresponding angles are addressed by using a transparency. By
tracing where one of the parallel lines crosses the transversal and sliding the transversal to match where the
other parallel line crosses the transversal the corresponding angles are identified. With these four special
angle pair names, now use examples and consider which are supplementary and which are corresponding. This
can be done through many ways, using the slopes of lines, measuring the angles, or tracing a transparency and
rotating it around throughout the diagram to determine angle correlations. Address the idea that transversals
can cut any two lines they don’t necessarily have to be parallel lines. Consider the diagram. Let n and m be
parallel lines and let m<1= 110º. Find the measures of the remaining angles.

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:
-What are the different special angles of two lines cut by a transversal?
-Do the lines cut by a transversal have to be/not be parallel?
-When a transversal does cut two parallel lines there are at most how many different measures of angles
throughout the 8 angles?
Assessment: Assessment will be accomplished by student responses and feedback during the lesson to
discover the level of classroom understanding by taking note of the areas students struggle or do not answer
correctly. Practice problems will be completed after the lesson.
Practice Problems:
1. Complete the missing angles in the following picture.
2. In the next two pictures state the exterior angles, interior angles, consecutive interior angles, alternate
exterior angles, alternate interior angles, and corresponding angles.
Adaptations:
In this lesson I will mention things for the students to consider throughout the lesson such as that keep the
advanced students engaged and thinking while still staying on task for those who need more help. Such as when
we are discussing the number of different angle measurements when two parallel lines are cut by a transversal
there response will most likely be 2. Continue their thought process to have them wonder “are there always
going to be exactly two angle measurements? Could you think of any instances in which there would not be
exactly two angle measurements”.
Follow-up Lessons/Activities:
A follow up lesson to this lesson would be exploring the postulates and theorems that correlate with parallel
lines being cut by a transversal. Also, solving algebraic equations to solve for the special angles in a pair of
parallel lines cut by a transversal would follow this lesson.