Kerri Bernhardt's Unit Plan


I. Congruent Triangles

II. Unit Objectives 

III. Specific Objectives

IV. Lesson Plans

Lesson 1:  Congruent Figures

The student will learn to recognize congruent figures (especially triangles) and their corresponding parts.  This lesson will consist of an activity with sliding, flipping and turning shapes and discussing congruent polygons.  Then the class will work on different problems with polygons and determining if they are congruent. 

Lesson 2:  Triangle Congruence by SSS and SAS (Full Lesson Plan)

The student will learn how to prove two triangles congruent using multiple postulates and theorems.  The students will use spreadsheets to solve problems and display data.  There will be an activity making triangles out of straws and discussing side lengths and making conjectures.  Next the students will work on proofs with the SSS and SAS postulate.  Spreadsheets will be used to compare side lengths and angle measures and then determine whether the triangles are congruent or not.  This computer activity will be done in class.

Lesson 3:  Triangle Congruence by ASA and AAS  (Full Lesson Plan)

The student will learn how to prove two triangles congruent using multiple postulates and theorems.  The students will practice and refine knowledge and skills in multimedia to create diagrams that relate to congruent triangles.  The lesson will have the students use construct triangles, cut them out, and make conjectures about them to investigate the ASA postulate.  Next the students will work through proofs using the ASA postulate and actually prove the AAS theorem.  Applications like Publisher and Word will be used to draw diagrams and explain SSS, SAS, ASA, and AAS.  This computer activity will be done in a computer lab.

Lesson 4:  Using Congruent Triangles:  CPCTC

The student will learn how to draw other conclusions after proving two triangles are congruent.  The students will practice and refine knowledge and skills in word processing to prepare outlines of proofs of congruent triangles.  The lesson will include a discussion of how SSS, SAS, ASA, and AAS can lead to CPCTC.  The students will work with CPCTC to solve real life problems.  The outline feature of a word processor will be used to write proofs, and unscramble parts of proofs.  This computer activity will be done in a computer lab.

Lesson 5:  Isosceles and Equilateral Triangles

The students will be able to use and apply properties of isosceles triangles.  The students will practice and refine knowledge and skills in multimedia to create diagrams that relate to congruent triangles.  This lesson will include an investigation activity of constructing isosceles triangles and making conjectures.  Three theorems about isosceles triangles will be discussed and proven.  Two corollaries about equilateral triangles will be discussed.  The students will go to the computer lab and use a program like Inspiration or Publisher to create diagrams of the theorems about isosceles triangles.

Lesson 6:  Congruence in Right Triangles

The students will be able to prove two right triangles are congruent using the Hypotenuse-Leg theorem.  The students will select and use technological tools for class assignments.  This lesson will have a discussion about right triangles and the parts of a right triangle will be defined.  The class will prove the hypotenuse-leg theorem, and use the HL theorem to prove other problems.  The students will go to the computer lab and use Geometer’s Sketchpad to investigate right triangles.

Lesson 7:  Using Corresponding Parts of Congruent Triangles

The students will be able to use CPCTC to identify congruent overlapping triangles.  The students will be able to use CPCTC to prove two triangles congruent by first proving two other triangles congruent.  This lesson will include identifying congruent overlapping triangles (on paper and using cut-outs) and use them to solve a problem about the Statue of Liberty.  The students will prove two triangles are congruent using two other triangles.  There will be an activity with kites and proving different triangles congruent. 

Lesson 8:  Review

The students will compete in a game using dry-erase boards to review topics in the chapter.  Different problems from all of the previous lessons will be given and the team with the most correct answers will be given extra credit.  The classroom computer and projector will be used to project the problems for the review game.


V. Introductory Resources

VI. Higher Order Thinking Skills

VII. Materials/Resources Available/Needed

VIII. Equipment Needed

IX. Evaluation

X. Time Period

Unit Plan Author: - Kerri Bernhardt / Back