Download Lesson Plan: Criteria for Triangle Congruence

Lesson Title: Criteria for Triangle Congruence
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 2
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
G.CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, AAS, and SSS) follow from the
definition of congruence in terms of rigid motions.
MP3: Construct viable arguments and critic the reasoning of others.
MP5: Use appropriate tools strategically.
MP7: Look for and make use of structure.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Give students 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 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?
Discuss with the class 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. Explain to students that they will be working through 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 -10 minutes at each station. Make sure
each station has 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?
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*Station Three- If only given AB  14.7 cm,  B  92 , and  C  54 , will
all triangles created be the 
same?
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*Station Four- If only given  A  34 ,  B  92 , and  C  54 , will
all triangles created be the same?
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*Station Five- If only given AB  14.7 cm, AC  18 cm, and BC  10 cm, will
all triangles created be the same?
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HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
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Lesson Title: Criteria for Triangle Congruence
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 2
Start/end times: _________________________
*Station Six- If only given AB  14.7 cm, AC  18 cm, and  C  54 , will
all triangles created be the same?
2. Allow students to investigate each station using the construction tools and given parameters. Encourage
students to make as many sketches as possible to come up with varying examples for each scenario.
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Once groups have discussed their findings, instruct students to record their observations on the
recording sheet and end each station by forming a final conjecture outlining their results. (Look for
evidence of use of MP5 and MP7.)
3. After students have rotated through the stations, bring the class back together to discuss their findings.
Discuss which stations led to multiple triangles and which stations always produced congruent
triangles. (Look for evidence of MP3.)
4. Ask students, “Based on what we discovered today what criteria should allow us to conclude that two
triangles are congruent and what criteria would be insufficient to determine congruence of triangles?”
Have the students generalize these findings into SSS, SAS, ASA, and AAS as well as discounting AAA
and SSA.
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?
Homework: Exactly what follow-up homework tasks,
problems, and/or exercises will be assigned upon the
completion of the lesson?
Paper, patty paper, ruler, and protractor.
Solutions to stations page
Station Investigation Recorder Sheet
(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.)
Homework should involve problems where students
are asked to identify if SSS, SAS, ASA, AAS apply.
If any do apply, the students should write congruence
statement for all pairs that are congruent. If none
apply, that should be stated.
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.