Lesson Title: _____Similar Parts Investigation_______________ Course: ___________CC Geometry___________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides
the other two sides proportionally, and conversely; and the Triangle Midsegment Theorem proved using
triangle similarity.
Lesson Launch Notes: Exactly how will you use the
first five minutes of the lesson?
Review applications of the Triangle Midsegment
Theorem. Sample problem:
In the figure below, KHL is the midsegment triangle
of GHJ. Name the relationship between as many
parts of this figure as you can.
H
Lesson Closure Notes: Exactly what summary activity,
questions, and discussion will close the lesson and provide
a foreshadowing of tomorrow? List the questions.
1. Has your answer to the last question changed
based on this exploration? Why or why not?
2. State your findings about similar triangles in
your own words.
[UDL III: 9]
K
G
L
J
[UDL I: 2,3]
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
Figure 2-1 below shows PQR and four identical copies. Arrange the four copies of PQR so as to create
a triangle similar to it. (You may copy, cut out, and use the copies.) Try the same method for XYZ in
Figure 2-2 when finished. (See Student Resource Sheet)
Figure 2-1
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: _____Similar Parts Investigation_______________ Course: ___________CC Geometry___________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Figure 2-2
3. Did the same method work for both triangles? If not, explain why not. If so, will this method work
for any triangle? Explain your answer.
4. Now cut out an arbitrary triangle from a piece of patty paper. Consider this triangle to be the “final
product”—that is, a large triangle that has been formed out of 4 smaller, similar triangles. Fold the
paper so as to reveal the 4 smaller triangles. Has your answer to the last question changed based on
this exploration? Why or why not?
[UDL II: 4,5,6]
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.
By the end of the lesson, students should have a deepened conceptual understanding of the relationship between
parts of similar triangles, i.e. corresponding sides are proportional and corresponding angles are congruent. This
investigation should cause them to see that by placing the different angles from three of the small triangles in the
same relative positions in the larger triangle as they were in the original triangle, they can easily form a similar
triangle. This proves the AA Triangle similarity postulate. The fourth one will then fit nicely in the middle. Because
the fourth triangle has to be turned upside down, its base is then parallel to the base of the larger triangle and it is
also a midsegment. This makes the corresponding sides of the original triangle and the larger one that they formed
proportional, verifying the SSS Triangle Similarity Postulate and the Triangle Midsegment Theorem.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Students should be familiar with the attributes of similar triangles and should be reminded of what happens when a
midsegment is drawn within a triangle. They should be encouraged to verify the side and angle relationships.
[UDL I: 2,3]
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.
Lesson Title: _____Similar Parts Investigation_______________ Course: ___________CC Geometry___________
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Resources: What materials or resources are essential Homework: Exactly what follow-up homework tasks,
for students to successfully complete the lesson tasks or problems, and/or exercises will be assigned upon the
activities?
completion of the lesson?




(To be determined by the teacher)
Similar Parts Student Resource Sheet
Protractor
Patty Paper
Scissors
[UDL II: 4]
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Ask: “How has this investigation helped you to understand the relationship between corresponding
parts of similar triangles? Write down any new or reaffirmed understandings that you gained.”
HCPSS Secondary Mathematics Office (v2); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student
achievement. Portsmouth, NH: Heinemann.