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Jencen Smith
Math Methods Unit on Geometry
Unit Title: Same Shape Shapes
Unit Topic: Triangle Congruence
Grade Level: 9th
Length: 10 days
Class Length: 55 Minutes
The requirements are labeled in RED pen throughout the unit plan
Big Ideas:
 Knowing the different types of triangles
 Being able to see different relationships between triangles
 Angle Relationships and the Triangle Sum Theorem
 Congruent Triangles
 Proving Triangle Congruence
Unit Essential Questions:
 What are the different types and triangles and how can we compare and
contrast them?
 How can we use angles within triangles to solve for the other angles and side
lengths within the triangles?
 How can we use our knowledge of angle relationships between triangles to
show that any two triangles are congruent?
 How can we use the SSS, SAS, ASA, AAS, HI, or CPCTC congruence theorems to
show that two triangles are congruent?
Unit Essential Topics/Daily Schedule:
Triangle Congruence: Students will learn about congruence and
transformations, classifying triangles, the triangle sum theorem, angle relationships,
and proving triangle congruence using a multiple theorems.
Sequence:
In this unit, the students will first have to understand what the different
types of triangles. We will have a lesson on all the types of triangles, where we will
learn to identify and compare the different types of triangles. Then we will have a
lesson on talking about angle relationships within triangles, which will prepare
them to create the triangle sum theorem. Because our next lesson will be on
congruent triangles, getting a refresher on congruence and how it relates to
transformations will jog their memory and help them connect the information. I will
do a lesson on congruence and transformations, which will show students that even
if we move a shape or object about the coordinate plane, it will still be congruent.
Then, we will talk specifically about congruent triangles. Then, we will have a day
where we have a short quiz over the first four lessons and then we will work with
some origami, where we will then see how what we have learned correlates with
origami. Then, we will have three lessons discussing the SSS, SAS, ASA, AAS, HL, and
CPCTC triangle congruence theorems, which will allow us to learn how to prove that
two triangles are congruent. After all of this, we will have a review lesson, where I
will have a review packet that we will go through to help the students study for the
next day’s test.
Day
1
2
Topic
Lesson Overview
In the first lesson, we will start
off with a warm up, where the
students will identify different
types of angles and solving for a
variable from side lengths of a
triangle. Then, the class will
translate their knowledge about
different types of angles and
Classifying
learn how each of these angles is
Triangles
directly related to a specific type
of triangle. They will take notes
on each of the definitions of an
acute, obtuse, equiangular, and
right triangle. Once they do this,
the class will work on a
classifying triangles based on
angle measures as well as side
lengths.
To begin this lesson, the
students will be given three
congruent triangles. They will
be told to prove that all three
angles inside a triangle add up to
180 degrees. This will lead into
the discussion about the triangle
Angle Relationships
sum theorem. From here, the
of Triangles and the
class will learn about two
Triangle Sum
corollaries to the triangle sum
Theorem
theorem. We will then talk
(FULL LESSON)
about the exterior angle
theorem. After this, the students
will work on a worksheet that
will help the students practice
using the theorems and
corollaries to solve for angles in
different triangles.
Common Core Standard
CC.9-12.G.CO.10:
Prove theorems about
triangles.
CC.9-12.G.CO.10:
Prove theorems about
triangles.
3
Congruence and
Transformation
4
Congruent
Triangles
5
Quiz and Origami
Lesson
(FULL LESSON)
In this lesson, we will be talking
about congruence and
transformations. Because the
students have already learned
about transformations, their
warm up will involve them
graphing a translation and a
reflection to refresh their brains.
Then, we will create a table,
representing transformations in
the coordinate plane with
translations, reflections,
rotations, and dilations. We will
go through an example of each
using the formulas that we had
come up with. After this, we will
talk about which
transformations produce
congruent images. The students
will then be asked to create
three different transformations,
two of which produce congruent
images, and one does not
produce a congruent image.
They will give them to a
neighbor and they will have to
determine which ones are
congruent images and which
ones are not.
This lesson is all about bringing
the past three lessons together
and using the theorems that the
class has learned to prove that
two triangles are congruent. We
will first talk about
corresponding angles and
corresponding sides. The class
will then prove that two
triangles are congruent using
the theorems that they had
learned in the previous three
lessons.
Right when the students walk
into class, they will take a quiz
over the first four lessons. This
CC.9-12.G.CO.6:
Use geometric
descriptions of rigid
motions to transform
figures and predict the
effect of a given rigid
motion on a given figure;
given two figures, use
the definition of
congruence in terms of
rigid motions to decide
if they are congruent.
CC.9-12.G.CO.7:
Use this definition of
congruence in terms of
rigid motions to show
that two triangles are
congruent if and only if
corresponding pairs of
sides and corresponding
pairs of angles are
congruent.
CC.9-12.G.SRT.5:
Use congruence and
similarity criteria for
triangles to solve
problems and prove
relationships in
geometric figures.
CC.9-12.G.SRT.5:
Use congruence and
similarity criteria for
6
Congruence
Theorems (SSS,
SAS)
will be used as a summative
assessment to see how well each
student understands the content
that is being taught. Once
everyone is done with the quiz,
we will grade them in class so
that each student knows how
they did, and knows what they
need more practice with. Then,
we will move into our “art
project” where each student will
be making some origami. They
will be given a worksheet with
the directions on how to make a
crane with a 3-inch by 3-inch
piece of paper. Once each
student makes a crane, we will
unfold them and study the
triangles that were created in
the paper. We will then prove
which triangles are congruent to
each other.
Now that the students
understand the idea how to
prove that two triangles are
congruent, we will discuss two
theorems that are shortcuts to
figure out if two triangles are
congruent. To start, the teacher
will make two triangles using
string and three different size
straws to prove the SSS and SAS
theorems. The students will
work through a worksheet that
will guide them through both
theorems given two congruent
triangles.
triangles to solve
problems and prove
relationships in
geometric figures.
CC.9-12.G.CO.8:
Explain how the criteria
for triangle congruence
(ASA, SAS, SSS) follow
from the definition of
congruence in terms of
rigid motions.
CC.9-12.G.SRT.5:
Use congruence and
similarity criteria for
triangles to solve
problems and prove
relationships in
geometric figures.
CC.9-12.G.CO.7:
Use this definition of
congruence in terms of
rigid motions to show
that two triangles are
congruent if and only if
corresponding pairs of
7
8
Congruence
Theorems (ASA,
AAS, HL)
Congruence
Theorems (CPCTC)
In this lesson, the we will go
through a similar process as the
previous lesson except we will
be discussing the ASA, AAS, and
HL theorems. We will go
through examples on a
worksheet that will guide
through these theorems. At the
end of this lesson, we will also
discuss why we cannot use SSA
to prove that two triangles are
congruent.
For our last lesson, we will bring
all the concepts together to talk
about how we can use
corresponding parts of
congruent triangles to show that
two triangles are, in fact,
congruent. To do this, we will
use the SSS, SAS, ASA, AAS, and
HL theorems. Using these, we
will be able to prove the CTCPC
theorem. Again, we will go
through a worksheet that uses
all five theorems to prove the
sixth theorem.
sides and corresponding
pairs of angles are
congruent.
CC.9-12.G.CO.8:
Explain how the criteria
for triangle congruence
(ASA, SAS, SSS) follow
from the definition of
congruence in terms of
rigid motions.
CC.9-12.G.SRT.5:
Use congruence and
similarity criteria for
triangles to solve
problems and prove
relationships in
geometric figures.
CC.9-12.G.CO.7:
Use this definition of
congruence in terms of
rigid motions to show
that two triangles are
congruent if and only if
corresponding pairs of
sides and corresponding
pairs of angles are
congruent.
CC.9-12.G.SRT.5:
Use congruence and
similarity criteria for
triangles to solve
problems and prove
relationships in
geometric figures.
CC.9-12.G.CO.8:
Explain how the criteria
for triangle congruence
(ASA, SAS, SSS) follow
from the definition of
congruence in terms of
rigid motions.
9
Review for Unit
Test
10
Unit Test
This day will be dedicated
towards reviewing for our test
the following day. The teacher
will create a review packet that
picks out important elements of
each lesson that will also appear
on the test. The students will
first work on the packet by
themselves. Then, the students
will pair up into pairs that the
teacher will create, based on the
class. During the last 15 minutes
of class, we will go through any
problem that students have
questions on.
The students will take their final
summative assessment for the
unit.
All Previous Common
Core Standards
All Previous Common
Core Standards