Lesson Title: Verifying Triangles are Congruent
Date: _____________ Teacher(s): ____________________
Course: Common Core Geometry, Unit 2
Start/end times: _________________________
Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which
Mathematical Practices do you expect students to engage in during the lesson?
G.CO.7 Use the 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.
MP1: Makes sense of problems and perseveres in solving them.
MP5: Use appropriate tools strategically.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Free response
Write down everything that you think of when you hear
the word congruence.
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and
connect big ideas? List the questions. Provide a
foreshadowing of tomorrow.
What, So What, Now What
Record your responses to the following prompts:
How can you prove two segments are congruent? two
angles?
What?
What have you learned?
So What?
What is the relevance to the unit we are studying?
Now What?
What can we do with this knowledge?
Where can we go from here?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students are working on during the lesson? Be sure to indicate strategic
connections to appropriate mathematical practices.
1. Preview Verifying Triangle Congruence and determine if it is necessary to provide students with the diagram
on the second page. Make copies and distribute the activity to each student.
2. Provide students with a variety of resources such as patty paper, graph paper, reflective tool, protractors, rulers,
and dynamic geometry software. Have students work in pairs or small groups to complete the activity. (Look
for evidence of MP1, MP5)
3. Conduct a class discussion using the following discussion questions: (Look for evidence of MP1)
 “How does a reflection, rotation, or translation affect the corresponding parts of a transformed figure?”
 “Is there a transformation that does not create a congruent figure?”
 “Using your prior knowledge of angles, side lengths, and triangles is there an alternative approach to
verifying the triangles are congruent besides showing that all of the corresponding sides lengths are
congruent and all of the corresponding angles are congruent.”
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 success? 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 the corresponding part of triangles and use them to determine if the triangles are
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: Verifying Triangles are Congruent
Date: _____________ Teacher(s): ____________________
congruent.
Course: Common Core Geometry, Unit 2
Start/end times: _________________________
Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc.
Vocabulary: corresponding sides and angles, congruence transformations, reflection, rotation, translation
Dilations are the only transformation studied that does not create congruent figures. This is due to the size change
which either increases or decreases the length of the corresponding sides.
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?
Verifying Triangle Congruence
Patty paper
Graph paper
Reflective tool
Protractors
Rulers
Dynamic geometry software
Choose three coordinates in three separate quadrants.
Graph the triangle using these coordinates. Choose a
center of rotation and transform the triangle using the
rotation algorithm. Verify that the corresponding parts are
congruent.
Using the same triangle, repeat the process above using
the translation algorithm.
Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson
standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson?
Are students able to construct accurate reflections, rotations, and translations?
Are students able to identify and verify the corresponding sides and angles are congruent?
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this
product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.