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```Subject Area: Algebra
Benchmark Period: III
Duration of Lesson: 1 hour
Standard(s): M&G3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are
congruent and what congruence means about the relationships between the sides and angles of figures.
Learning Objective: Students will determine whether or not two polygons are congruent.
Big Ideas involved in the lesson:
The nature of congruence
As a result of this lesson students will:
Know:
 Vocabulary: Polygon, line segment, endpoints, sides, vertex/vertices, congruent, corresponding sides,
corresponding angles, bisect, regular polygon, triangle, quadrilateral, pentagon, hexagon, diagonal,
consecutive/non-consecutive, angle, postulate
 How to write a line segment AB , an angle ABC , and a triangle ABC .
 How to write the measurement of an angle ( mA =…).
 The symbol for congruent (  ).
Understand:
 How to write an informal proof for the congruence of two polygons
 There are different methods to prove that two polygons (namely triangles) are congruent.
 That two polygons are congruent if their corresponding sides and their corresponding angles are
congruent. (They must be same shape and same size).
 That a number of diagonals can be drawn depending on the number of sides of the polygon.
 Diagonals can be drawn to help prove that polygons are congruent.
 Regular polygons (i.e. Regular hexagons) are not always congruent, though they have congruent angles.
Be Able To Do:
 Name angles, segments, and points.
 Name polygons by listing their vertices in order.
 Identify corresponding angles for congruent polygons.
 Identify congruent angles.
 Identify congruent sides of polygons.
 Identify corresponding sides for congruent polygons.
 Write an informal proof for congruent polygons.
1
M&G 3.4
Assessments:
What will be
evidence of
student
knowledge,
understanding
& ability?
Formative: ABWA
Checking for
understanding during
lesson
Independent Practice
(Teacher created
worksheet)
CFU Questions
 What is congruency?
 Why is knowing if two shapes are congruent important?
 How do we name lines?
 How do we name segments?
 How do we name rays? How do we name angles?
 How do we identify a triangle by its sides?
 How do we identify triangles by their angles?
Summative:
 How do we differentiate between polygons?
Teacher created
 Tell me whether or not each pair of triangles is congruent. If
quiz/test, DWA, CST
they are congruent, write a statement of congruency and tell me
how you know that they are congruent.
 Are the parallelograms pictured below congruent? How do you
know this?
 What information is necessary to prove two triangles congruent?
 What information is necessary to prove to polygons congruent?
Lesson Plan
Anticipatory Set:
Show powerpoint anticipatory set file - add more real life reasons for learning
a. T. focuses students
congruency if you deem it appropriate or needed.
b. T. states objectives
c. T. establishes purpose of CFU – What are we going to learn? Why are we going to learn this?
the lesson
d. T. activates prior
Preview/Review – As this lesson is to be implanted in a 7th grade honors Algebra
knowledge
1 course, it may not occur directly after another geometry lesson. So a review of
some geometric terms may be necessary. See the attachment Preview-Review
M&G3.4 file. Project the file and go over with students.
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for Understanding
 Pose key questions
explain concepts,
definitions, attributes in
their own words
 Have students
discriminate between
examples and nonexamples
 Encourage students
generate their own
2
CFU Questions – How do we name lines? How do we name segments? How do
we name rays? How do we name angles? How do we identify a triangle by its
sides? How do we identify triangles by their angles? How do we differentiate
between polygons?
All instruction is included in a form that is ready for projection. It is in the file
M&G3.4 instruction.
CFU Questions (in above file):
On your white board, tell me whether or not each pair of triangles is
congruent. If they are congruent, write a statement of congruency and tell
me how you know that they are congruent.
Are the parallelograms pictured below congruent? How do you know this?
M&G 3.4
examples
 Use participation
Guided Practice:
a. Initiate practice activities
under direct teacher
supervision – T. works
problem step-by-step
along w/students at the
same time
b. Elicit overt responses
from students that
demonstrate behavior in
objectives
c. T. slowly releases
student to do more work
on their own (semiindependent)
d. Check for understanding
that students were
correct at each step
e. Provide specific
knowledge of results
f. Provide close monitoring
What opportunities will
mathematics?
Closure:
a. Students prove that they
know how to do the work
b. T. verifies that students
can describe the what
and why of the work
c. Have each student
perform behavior
Independent Practice:
a. Have students continue
to practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
3
Teacher and Students begin working guided practice (See file M&G 3.4 Guided
Practice.doc) together. Teacher gradually releases the students to do the
problems on their own.
CFU – What information is necessary to prove two triangles congruent? What
information is necessary to prove to polygons congruent?
Lecture, note-taking, pair-shares and written
responses during CFUs, guided practice, etc.
Review vocabulary and concepts learned. Have students do 2 exit problems on
post-it notes or scratch paper and have them turn it in on their way out (this way
the teacher can tell if re-teaching is needed).
On board, teacher draws two triangles with sides measuring 3, 8, 13 with different
orientations.
1) Determine if the two triangles are congruent. If they are, write a statement
telling why they are congruent.
On board, teacher draws a regular quadrilateral, ABCD.
2) Draw a diagonal, BD, and prove that  ABD   CDB.
See M&G 3.4 Independent Practice file.
M&G 3.4
Resources: materials
needed to complete the
lesson
4
M&G 3.Anticipatory Set file.
M&G 3.4 Instruction file.
M&G 3.4 Guided Practice file.
M&G 3.4 Independent Practice file.
M&G 3.4
```
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