Lesson Title: Triangle Congruence (SSS, SAS, ASA, AAS)__________ Course: Geometry
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
G.CO.8: Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
In the first three minutes students are given two
diagrams. One diagram with 2 congruent triangles
(showing all corresponding sides and angles congruent)
and one diagram with 2 triangles that are not congruent
where the two triangles have one pair of congruent
sides labeled and three non congruent angles. Students
are asked to write a congruence statement for the two
diagrams.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
What information allows us to conclude that two triangles
are congruent? How does knowing this information help
us as we move forward in trying to prove two triangles are
congruent?
The class will discuss why it was impossible to write a
congruence statement for the second diagram. The
teacher should ask if it was necessary to see that all
three angles were not congruent, or if less information
was needed, to conclude that the triangles could not
possibly be congruent. (UDL:I.3), (UDL:II.6),
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Lesson Launch – This will help to activate students’ prior knowledge about corresponding parts on
congruent triangles and writing congruence statements. It will also be used to open up a discussion that it
may not be necessary to know all parts of two triangles in order to prove them congruent.
2. Introduction of Task – Explain to students that there are six stations. At each station they will be given
three measurements and will be asked to decide if these measurements will always produce congruent
triangles or if there are multiple triangles that could be formed using the measurements given.
Place students in rotating groups that will be given approximately 6 minutes at each station. Each station
will have paper, patty paper, rulers, and protractors.
The stations are set up as follows:
*Station One- If only given AB  14.7 cm, AC  18 cm, and  A  34 , will
all triangles created be the same?
*Station Two- If only given  A  34 , AB  14.7 cm, and  B  92 , will
all triangles created be the same?



*Station Three- If only given AB  14.7 cm,  B  92 , and  C  54 , will
all triangles created be the 
same?


*Station Four- If only given  A  34 ,  B  92 , and  C  54 , will
all triangles created be the same?



*Station Five- If only given AB  14.7 cm, AC  18 cm, and BC  10 cm, will
HCPSS Secondary Mathematics Office (v2); adapted
from: Leinwand,
S. (2009). Accessible mathematics:
10 instructional shifts that raise student

achievement. Portsmouth, NH: Heinemann.



Lesson Title: Triangle Congruence (SSS, SAS, ASA, AAS)__________ Course: Geometry
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
all triangles created be the same?
*Station Six- If only given AB  14.7 cm, AC  18 cm, and  C  54 , will
all triangles created be the same?
3. After students have rotated through the stations bring the class back together to discuss their findings. Discuss
 congruent triangles. (UDL:III.8),
 and which stations
 always produced
which stations led to multiple triangles
4. Ask the students, “Based on what we discovered today what information should allow us to conclude that two
triangles are congruent and what information would still leave us wondering?” Have the students generalize these
findings into SSS, SAS, ASA, and AAS as well as discounting AAA and SSA. (UDL:I.2), (UDL:I.3),
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will be able to identify that two triangles are congruent based on SSS, SAS, ASA, and AAS.
In future lessons students will be able to use these concepts to prove that two triangles are congruent.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Students may have misconceptions about what each abbreviation truly stand for. For instance, they may not know
what it means for an angle to be “included” when attempting to use or identify SAS.
Resources: What materials or resources are essential
for students to successfully complete the lesson tasks or
activities?
Paper, patty paper, ruler, and protractor.
-The teacher could precut “segments” and “angles” so
students need only manipulate these object and then
draw in the rest, versus having to draw/measure new
segments and angles at each station. (UDL:I.1),
(UDL:II.4,5), (UDL:III.7), (UDL:III.8)
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Homework should involve problems where students are
asked to identify if SSS, SAS, ASA, AAS apply. If any
do apply the students should write a congruence statement
for all pairs that are congruent. If none apply that should
be stated. (UDL:I.3), (UDL:III.9)
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Do my students know the four ways to prove triangles congruent that were discussed today?
Can my students identify when these postulates/theorems can be used or do not apply?
Looking forward to the next day’s lesson, will my students be able to apply these postulates/theorems to complete
proofs involving triangles?
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Triangle Congruence (SSS, SAS, ASA, AAS)__________ Course: Geometry
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.