Name: Jeremy Lee

 

Title of Lesson: Triangle Congruence

 

Date of Lesson: TBA                      

 

Lesson Length: 1 hour

 

Description of class:

            Grade Level: High school

 

The Lesson:

 

I. Overview

The students will explore the triangle congruence. They will create triangles given certain restrictions and then compare their triangles with classmates. Then as a group, we will make the determination if SAS, SSS, AAS, and ASS are true conjectures.

 

II.    Performance or Learner outcomes

The students will be able to prove a theorem. The students will be able to rely on prior knowledge about triangles to prove conjectures. They will be able to work in groups and compare to determine if the conjecture is true for every case. The students will be able to come up with counter examples to disprove a theorem.

 

III.      Supplementary materials, handouts- three worksheets see attached

 

IV.      Five E Organization

Teacher Does

Student Does

Engage:

The teacher first arranges the students into groups of four. The teacher then leads a discussion, which reviews what the students know about congruent triangles. The teacher then describes a proof and challenges the students to prove SSS conjecture. Then the teacher will give each group worksheet 1.

Questions?

What do you know about triangles?

What do you think; can we make more than one triangle given the lengths of all three sides?

 

The students will get into groups of 4 and brainstorm about triangles.

 

 

 

 

 

Expected Answers

-       180, the side opposite the biggest angle is the biggest

-       Yes, No
Evaluate

The teacher should have called on different students to give more description about the knowledge of triangles. The teacher will facilitate the knowledge discussion about triangles.

 

Explore:

Tell the students to follow instructions on the worksheet.

After the students compare have them return to their desks.

Explain

Questions:

Did anyone find a ÒdifferentÓ triangle from your neighbors?

 

From our discussion about triangles what has to be true for two triangles to be congruent?

So if it is facing a different way, is it congruent?

Explore: Now we have proven that if three sides are the same, then the two triangles are congruent.

 

The teacher will then hand out the ASA worksheet.

The students will work in the same groups to try to prove congruent triangles.

After they have constructed the triangles, compare with the group. The teacher will ask the groups why this works for every triangle

The teacher will then have one person present to the class.

 

The students check over their tables. They discuss between their groups and create a conclusion as to SSS conjecture. Then they will take their triangles to other groups in the class and compare.

Expected Student Answers

  1. No, if yes, mine was in a different direction
  2. Same side measures and same angles.
  3. Yes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Evaluate

The Teacher will watch each group carefully and make sure each student understands how to Construct the triangles. The teacher will make sure the students understand by making sure they can explain their reasoning fully.
Explain: The student will present their findings to the class.

 

Questions: Will all of these conjectures work?

 

Ok Well, I have always been told that ASS is a word that is not allowed in class, so that is why we cannot use it to prove congruence.

Now we must prove that if two triangles have an angle and two sides (not including the angle) that those two triangles are not congruent.

 

 

 

 

 

 

 

 

 

 

Yes, it seems like it.
Evaluate

The teacher will let each group explain their triangles fully. The teacher will make sure that students not presenting are paying attention by randomly asking questions.

 

Extend/Elaborate

The teacher will then give the students the SAS, and AAS Worksheets for homework.

Give the students the hint to use other things we have used in class to prove these.

 

At the begging of next class have two students present their answers.

 

 

Challenge Problem:

Ok Well, I have always been told that ASS is a word that is not allowed in class, so that is why we cannot use it to prove congruence.

Now we must prove that if two triangles have an angle and two sides (not including the angle) that those two triangles are not congruent. Due in one week.

 

 

Do the worksheets for homework. If they have time or want extra credit, they will do the challenge problem as well.