## Testing for Congruent Triangles

### Johnny WolfeSanta Rosa District Schools

#### Description

Students test triangles for congruency.

#### Objectives

Uses properties and relationships of geometric shapes to construct formal and informal proofs.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Testing for Congruent Triangles (see attached file)

- Scissors

- Paper for cutting out triangles

- Testing for Congruent Triangles Examples (see attached file)

- Testing for Congruent Triangles Worksheet (see attached file)

- Testing for Congruent Triangles Checklist (see attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Testing for Congruent Triangles Examples (see attached file).

2. Have marking pens (for overhead).

3. Have scissors and paper to cut triangles for students.

4. Have Testing for Congruent Triangles Examples (see attached file) prepared and ready to demonstrate to students.

5. Have enough copies of Testing for Congruent Triangles Worksheet (see attached file) for each student.

6. Have enough copies of Testing for Congruent Triangles Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations. Note: This lesson contains a checklist to assist the teacher in determining which students need remediation. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation.

1. Discuss why congruency is important (see # 1 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

2. Have students create a pair of congruent triangles (see # 2 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

3. Discuss corresponding parts between congruent triangles (see # 3 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

4. Discuss CPCTC (see # 4 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

5. Work example 5 (see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

6. Work example 6 (see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

7. Prove that congruence of triangles is reflexive, symmetric, and transitive (see # 7 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

8. Discuss the SSS Postulate (see # 8 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

9. Work an example using SSS Postulate (see # 9 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

10. Work example #10 (see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

11. Work example #11(see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

12. Discuss the SAS Postulate (see # 12 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

13. Work an example using SAS (see # 13 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

14. Work example #14 (see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

15. Work example #15 (see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

16. Discuss ASA Postulate (see # 16 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

17. Work an example using ASA Postulate (see # 17 on attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

18. Work example #18 (see attached file Testing for Congruent Triangles Examples). Answer student questions and comments.

19. Distribute the Testing for Congruent Triangles Worksheet (see attached file).

At this time, the teacher will need to collect the student's work and assess using the Testing for Congruent Triangles Worksheet Key. It may be helpful to use the additional checklist provided for Teacher Use Only to help determine which students need remediation and in which areas need addressing.

20. Distribute the Testing for Congruent Triangles Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST. Allow students time to reflect on their work.

21. The student will write their response on the worksheet.

22. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and assessed according to “Testing for Congruent Triangles Checklist”. If sufficient practice has been provided for stuents, these scores may be placed in the grade book. If this is the first time students have received practice in this area, it is recommended that handouts be formatively assessed.

#### Extensions

Write SSS, SAS, and ASA on three index cards. Have volunteers come to the front of the room one at a time, choose a card, and give an example of the postulate to the class.