Teacher: Kerri Bernhardt Lesson Topic: Triangle Congruence using ASA and AAS
Level: 10th grade
NCSCOS Goal and Objective(s): Mathematics-The student will learn how to prove two triangles congruent using multiple postulates and theorems. (NCSCS 2.03 a) Computer- The learner will demonstrate knowledge and skills in the use of computer and other technologies. (NCSCS 2.01)
Prerequisite Background Knowledge/Preassessment (information needed for students to benefit from lesson):
The students must know the meaning of included for both sides and angles. The students will need to know what congruent means and properties that can be used to prove triangles are congruent.
Materials/Resources/Technology: Protractors, compasses, scissors, computer lab with publisher and word or similar applications, textbook, paper and writing utensil, projector
Procedures (beginning, middle, end – comprehensive step-by-step explanation of teacher and student activities):
The lesson will begin with an investigation activity of the ASA postulate. The students will draw a triangle and label it ABC. Next they will construct a segment XY congruent to AB, angle X congruent to angle A, and angle Y congruent to angle B. Finally they will label the other point on this triangle Z. The students will then cut out the triangles and investigate congruence. Next a conjecture will be made about these two triangles and their similarities will be discussed.
There will be a discussion of the differences between SAS and ASA (sides vs. angles). The ASA postulate will be defined. Next a proof will be done using the ASA postulate. The angles and sides of a lacrosse goal will be used to write a proof using ASA.
The class will walk though the steps of a flow proof of the AAS theorem using the ASA postulate. Next the AAS theorem will be defined. Next the class will write two proofs using the AAS theorem.
the class will travel to the computer lab and use applications like
and Word to draw diagrams and write explanations of SSS, SAS, ASA, and
Thinking Question: Create an outline proof of the
Angle Side Angle postulate.
Differentiation (What will the teacher do to meet the needs of the various learners in your class?):
The investigation activity helps the students visualize the ASA postulate. The computer activity makes a visual and explanation in the students own words of the different theorems and postulates used.
Assessment (How will the teacher know students learned?):
The computer activity will be collected and assessed to determine students understanding.
Remediation/Next Steps (What will the teacher do for students who did not meet expectations? Also, what will the students do for follow-up/Homework/Enrichment?):
Students who did not meet expectations will be given another assignment of problems and written explanations after a review of the topics covered. All students will be assigned a number of homework problems to ensure their understanding.
successful? What should be
done differently regarding classroom management, instructional
Kerri Bernhardt: Back