Download File - Geometry

Triangle Congruence
Indirect Lesson
Topic: Triangle Congruence Postulates
Duration: 90 minutes
Materials: 10 Envelopes with 8 triangles in each (4 congruent pairs), activity worksheet, notes
worksheet, exit slip, homework worksheet
Michigan State Standards/Benchmarks:
G2.3.1 Prove that triangles are congruent using the SSS, SAS, ASA, and AAS criteria and that right
triangles are congruent using the hypotenuse-leg criterion.
Objectives:
SWBAT:
- Determine triangle congruence using SSS, SAS, ASA, and AAS congruence theorems given two
triangles.
- List corresponding angles and sides between congruent triangles.
- Create proofs to show triangle congruence.
Purpose:
The purpose of this activity is for students to discover the congruence theorems that are such an
integral part of triangle parts. They will use these theorems over and over, so the idea of this activity is
to reach as many types of learners as possible using a hands-on group activity, discussion, and notes.
Anticipatory Set:
I can:
- Determine triangle congruence using SSS, SAS, ASA, and AAS congruence postulates given the
corresponding information.
- Prove triangle congruence using a two column proof.
Exploring the Concept/Find Patterns/Create Understandings:
Students will be in groups of 4. They will be given an envelope with 8 triangles inside. They will then be
asked to group the triangles into congruent pairs using the information written on the triangles. Each
congruent pair will be marked with information that will depict a different congruence postulate. For
example, ∆ABC and ∆LMN are two congruent triangles. In order to show SSS congruence postulate, they
would be marked with three corresponding sides 3, 4, 5. Both the triangles would have their
corresponding sides marked with 3, 4, and 5.
Students will be asked on their worksheet to pair them and draw them. They will be asked to make sure
to draw the corresponding parts as well. Then students will look at the order of the corresponding parts
in those triangles and list them. For example, in congruent triangles ∆ABC and ∆DEF ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐷𝐸 (side),
̅̅̅̅ ≅ ̅̅̅̅
B ≅ E (angle), 𝐵𝐶
𝐸𝐹 (side). They will do this for each of their triangle pairs.
Expected time duration:
Group triangles = <5 minutes
Draw/mark triangles = <5 minutes
List corresponding parts = <10 minutes
Total time = <20 minutes
Metacognition Opportunities:
Once they have listed these as a group, students will be asked to draw their triangle pairs on the board,
along with the list of corresponding parts, ie. side, angle, side as in the example above. Once all the
groups have done this, I will direct a short discussion.
Questions to ask:
What do you notice about the lists of corresponding parts?
Are they all the same?
What do the lists show about their triangles?
Can you make any conclusions about these lists?
Write on board:
 Side-Side-Side (SSS) Congruence Postulate – If three sides of one triangle are congruent to three
sides of a second triangle, then the two triangles are congruent.
 Side-Angle-Side (SAS) Congruence Postulate – If two sides and the included angle of one triangle
are congruent to two sides and the included angle of a second triangle, then the two triangles
are congruent.
 Angle-Side-Angle (ASA) Congruence Postulate – If two angles and the included side of one
triangle are congruent to two angles and the included side of a second triangle, then the two
triangles are congruent.
 Angle-Angle-Side (AAS) Congruence Postulate – If two angles and a nonincluded side of one
triangle are congruent to two angles and the corresponding nonincluded side of a second
triangle, then the two triangles are congruent.
Expected time duration:
List on board = <10 minutes
Discussion = <10 minutes
Listing postulates on board = <10 minutes
Total time = <30 minutes
Opportunities to Apply Learning to New Situations:
Students will have the opportunity to use these congruence theorems beginning in their homework for
this class. They will be using these theorems for reasons as they prove triangle congruence.
Checking for Understanding:
Show students pairs of congruent triangles with corresponding parts marked and ask which congruence
postulate proves them to be congruent.
Assessment:
Students will complete a worksheet that begins with proof examples using the postulates. Then students
will complete the worksheet for homework. There will be a proof near the end, but students will not be
held accountable since we did not have time to discuss them in the previous class.
Closure:
Students will be asked to fill out an exit slip before leaving class to answer these questions:
1. What helped you learn today?
2. What did not help you learn today?
3. What did you learn today?
4. List a question you still have about triangle congruence:
Adaptations/Differentiation:
Students with accommodations and/or IEPs have additional time to complete the assignment.
Depending on their plan, they may have up to 2 additional class periods to turn it in.