Lesson Plan: Proving Triangles Congruent by SAS, SAS, ASA, AAS
I. Standards: 2.9.G.A, 2.9.G.B, 2.4.G.A, 2.5.G.A, 2.5.G.B
2.4.G.A: Write formal proofs (direct, indirect, proofs by contradiction, use of
counter-examples, etc.) to validate conjectures or arguments.
2.5.G.A: Develop a plan to analyze a problem, identify the information needed to
solve the problem, carry out the plan, check whether an answer makes sense, and
explain how the problem was solved in grade appropriate contexts.
2.5.G.B: Use symbols, mathematical terminology, standard notation,
mathematical rules, graphing, and other types of mathematical representations to
communicate observations, predictions, concepts, procedures, generalizations,
ideas and results.
2.9.G.A: Identify and use properties and relations of geometric figures; create
justifications for arguments related to geometric relations.
2.9.G.B: Use arguments based on transformations to establish congruence or
similarity of 2-dimensional shapes.
Goal: The goal of this lesson is to have students apply their knowledge of congruence
to prove two or more triangles congruent. The students will write proofs for proving
Students will be able to identify given information about the sides and angles of
Students will be able to properly label the triangle with the standard mathematical
symbols from the measurements given.
Students will be able to analyze the given measurements and apply the methods of
proving triangles congruent.
Students will be able to construct proofs to prove triangles congruent using the
correct mathematical terminology and representation.
SEE NOTES ATTACHED TO LESSON PLAN (PAGES 1-7)
i. Warm up activity
ii. Examples from http://www.nexuslearning.net/books/ML-
1. Students will form into pairs.
2. Then the students will working with their partner with the teacher
as an aide monitoring their performance. Students will work on the
guided proofs of SSS, SAS, ASA, AAS. From
3. The mathwarehouseprobelms will help the students prove
trianglescongruent and ask why triangles are not congruent. They
will also practice their skills in formally writing geometric proofs.
This technology acts as a guide.
4. Homework. Worksheet from the website below. Students will state
how they know triangles are congruent, and the students will
practice identifying the given information to see if the triangle can
be proven congruent.
V. Student Evaluation:
a. Students will work on/complete the online work with their classmates. They will
be able to work together and convey their ideas to one another.
b. Before leaving the teacher will come by to check and make sure the students have
given a good effort on the worksheet based on the teacher’s judgment.
c. The rest of the worksheet will be given as homework.
Strengths: I thought a strength was my examples. I thought I showed a lot of examples and went
through them all step-by-step during the lesson plan. I also thought my examples were of the
same difficulty level of the in-class assignment and the homework worksheet. It is always
important (I think) to make sure the students are confident in the work before they attempt the
homework. So I think I prepared the students for the homework with my lesson and its examples.
Another strength I thought I had in my lesson was clarity and a logical thought process. I thought
I did a good job in transitioning from the concept of congurnet triangles to using theorems and
postulates to prove different triangles congruent. I thought my proof process was clear,
understandable and easy to duplicate from a students perspective.
Weaknesses: I didn’t manage my time well. When I practice my lesson the day before, I need to
time myself. I thought I needed to work on my eye contact better. It’s a lot of drawing on the
board; however I caught myself talking to the board a few times. I also thought I could’ve added
a little more student interaction. But I felt that the technology piece I did not get too would’ve
incorporated student interaction. I thought I used questioning a decent amount, but maybe could
Make better eye contact
Practice talking to the students and with students rather than talking to the board.
Always be aware of the clock
Include more questioning