Hampton High SchoolGeometry Lesson Plan With Technology – Triangle Congruency Postulates

90 minutesMichelle Bousquet

Context: This lesson is designed for a 90 minute Geometry class at Hampton High School. The class contains a maximum of 21 students. This is the first lesson on triangles. The students will produce a representation via an online manipulative pertaining to triangle properties in order to learn during this lesson.

Objective: Students will correctly determine if there is enough information to prove that three different sets of triangles are congruent given at the end of the class period. If there is enough information, the students will accurately state the congruence postulate they would use.

SOL: G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent, using algebraic and coordinate methods as well as deductive proofs.

Materials/Resources: One laptop for every student Triangle Congruence Postulates Worksheet http://illuminations.nctm.org/ActivityDetail.aspx?ID=4

Content and Instructional Strategies:1. Briefly introduce the “Triangles” topic that the class will be learning about for the next

couple months. Explain that today students will learn about different ways to prove two triangles are congruent. Review definition of “congruent.” Pass out worksheet with practice problems. 5 minutes

2. Pass out one laptop per student, ask students to log in using their student identification number and password, and go to http://illuminations.nctm.org/ActivityDetail.aspx?ID=4. Note that even though this online manipulative is titled “Congruence Theorems,” we will not actually be proving the theorems, and thus we will refer to them as Triangle Congruence Postulates.5 minutes

3. Begin with the Side-Side-Side Congruence Postulate. Draw two triangles on the board with congruent sides. Explain that we will be determining if the side lengths alone can prove the two triangles are congruent. Introduce the website and how you can rotate and move sides and angles. On the Congruence Theorems website, have the students manipulate Side-Side-Side triangles to prove congruence. Then, have them try to make a triangle that is not congruent to the triangles that have already been made. Ask the class if any student is able to make a triangle that is not congruent to the others. We will find that it is not possible to make a triangle that is not congruent. Therefore, triangles can be congruent by Side-Side-Side. Repeat this activity with Side-Angle-Side, Angle-Side-Angle, and Angle-Angle-Side. As the class completes each congruence postulate, they will fill out the worksheet as guided by the teacher. For SAS, show on the board that if the angle changes, then the triangle has to change. 40 minutes

4. Continuing on the website, the students will use this manipulative to find that Side-Side-Angle and Angle-Angle-Angle do not guarantee that two triangles are congruent. On the board use a compass to show that two triangles can be made if two triangles have Side-Side-Angle. For Angle-Angle-Angle, describe that the triangles are considered similar, not congruent. 20 minutes

5. Students will complete the practice worksheet with the other classmates in their group. If they have enough time to finish the worksheet, they will turn it in for the teacher to assess understanding. Otherwise, they will finish it for homework and turn it in next class. 10 minutes

6. Students will put away laptops while the teacher reviews the four congruence postulates.10 minutes

Evaluation: The teacher will assess the students’ understanding of the new material by checking the practice problems. The students should answer 3/3 questions correctly.

Differentiation and Adaptations: The amount of time allotted for students to enter their student identification numbers and passwords into the laptops may take much longer than anticipated if there are laptop issues or a student does not remember his or her password. This may alter the time taken for the other activities. The class may not be able to go through every congruence postulate on the manipulative or the practice problems can be done for homework. If there is extra time, the teacher can create more practice problems or they students can continue using the online manipulative to reinforce concepts learned. If there is a student who is unable to work at a computer by him or herself, the students can work in groups.

If the computers fail to work or for some reason this website is not available on the school network, the students will learn the congruency properties of triangles by direct instruction from the teacher as guided by the worksheet. The students will be given triangles with each property and they will be challenged to draw triangles that disprove each property using a ruler compass. The students will still complete the practice problems on the worksheet.

National Council of Teachers of Math (2012). Congruence theorems. In Illuminations. Retreived from http://illuminations.nctm.org/ActivityDetail.aspx?ID=4

Name:____________________________________________ Date:_____________

Triangle Congruence Postulates

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.

If Side

Side and

Side

Then

SIDE-ANGLE-SIDE (SAS) CONGRUENCE POSTULATEIf 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.

If Side

Angle and

Side

Then

ANGLE-SIDE-ANGLE (ASA) CONGRUENCE POSTULATEIf two angles and the included side of one triangle are congruent to two angles and the included side of the second triangle, then the two triangles are congruent.

If Angle

Side and

Angle

Then

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.

If Angle Angle and

Side

Then

Note: Side-Side-Angle (SSA) and Angle-Angle-Angle (AAA) do NOT prove congruence between triangles. Practice:

For the following pairs of triangles, decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate you would use.

1.

2.

3.

Answer Key:

SSS Congruence Postulate:

SAS Congruence Postulate:

ASA Congruence Postulate:

AAS Congruence Postulate:

Practice:

1. Yes, SSS2. No3. Yes, SAS

Screenshots of Each Congruence Postulate and SSA and AAA

Reflection

1. In my lesson plan, I am able to provide multiple means of representation. First, the students will learn about the triangle congruency postulates visually by manipulating online triangles. Then, the students will verbally discuss the postulates and listen to the teacher reaffirm the theorems. I also provide multiple means of action and expression. The students will learn by manipulating online and completing problems on a worksheet.

2. The use of technology connects with the content focus because the online manipulative is able to create accurate angle measures that would take considerably more time if students were creating them themselves. Unless a teacher has time to break this lesson into multiple days or chooses to read off the postulates without any sort of student visual activity, this online manipulative is one of the only ways to create inquiry based learning with the students. This technology was made for the sole purpose of teaching the triangle congruence postulates, as well as the options that do not fulfill the postulates, like Side-Side-Angle and Angle-Angle-Angle.

3. The use of technology in my lesson play connects well with my student-centered approach to learning of producing a representation using a visual manipulative. The online activity provides student-centered inquiry-based learning. The students will discover the triangle congruency postulates for themselves by creating their own triangles before I teach the postulates.

4. The content, pedagogy, and technology “fit” together in the lesson because, in most cases, they are dependent on each other. Without the content, the online manipulative would not have a purpose. Without this pedagogy, there would not be a point in using an online manipulative to teach the postulates. Without technology, my pedagogy would be difficult to fulfill and the content would likely not be met in an inquiry based way.

5. The relative advantage of the technology used in the lesson is, like I stated earlier, that it is one of the only ways to teach this specific content in an inquiry-based way. The technology is self-explanatory and there is little needed to set up for class. The technology saves a lot of time from passing out and cleaning up hands-on manipulative.

6. This process helped me to zero in on appropriate and effective technologies to approach the lesson because I had to think about what technologies would really benefit the students more than traditional teaching. Math is a subject that has been taught using pencil and paper for centuries. By choosing to produce a representation using technology, I had to consider which sources of technology would truly be the best way to teach the triangle congruence postulates. The online manipulative I chose is perfect for this because it was created to teach this lesson and students can access this activity from most computers with Internet. They are likely to remember the content for a longer period of time because they will have discovered it themselves. Lastly, this site is much more entertaining than the typical teacher lecturing.