Congruent Triangles

Introduction

In this webquest you will be proving triangles congruency, along with their angles. Congruent triangles and their angles are very important when making bridges. You will be making a model bridge, you will need toothpicks and glue.

                                

Task

At the end of this WebQuest you will be able to prove triangles and their angles congruent by the following: making triangles congruent by using SSS, SAS, ASA, AAS, and HL theorem. You will also be proving their angles congruent by using CPCTC on some problems not all. You will need to make your own proofs according to the postulate given, along with the angles being proved. This isn't a partner assignment. You will be held accountable for the proof chart in the correct format.  At the wend you will also be constructing a bridge made from tooth picks. Remember, making a bridge depends on making all the lengths and sizes in a triangle equal for you to have a safe bridge. Read directions carefully!!!

Process

For this WebQuest I will give you pair of triangles to prove. On this website your are free to create your own if you wish. http://illuminations.nctm.org/Activity.aspx?id=3504.

You will be creating a word document with the proof chart, whith the columns labled: Statement, and Reasoning. You will be taken off points if it is not in the right format. You will be using  CPCTC proofs also. 

You will also be creating a bridge using triangles that are congruent to each other. You can use any type of triangle, but once again need to be congrent to each other. You will need glue and toothpicks.

This is not a partner assignment. You will have two days to complete the Webquest there will be no 

class time so use your time wisley.

Here is a example of a triangle congruency proof chart and an example of  CPCTC proof chart:

 

1.

Using the SSS Theorem: http://www.mathopenref.com/congruentsss.html                 

  • Prove: Δ ABC ≅ Δ CDA

Given: Side: AB ≅ Side: CD, Side: XD ≅ Side: CB

  • Using CPCTC

Prove: Side: AC≅ Side: AC

Given: Side: AB ≅ Side: CD, Side: XD ≅ Side: CB

 

2.

Using SAS Theorem: http://www.mathopenref.com/congruentsas.html

Prove: Δ JAK ≅ Δ NAK

Given: ∠ AKJ ≅ ∠ AKN

3.

Using ASA Theorem: http://www.mathopenref.com/congruentasa.html

Prove: Δ WZU ≅ Δ WXV

Given: ∠Z ≅ ∠X, Side: WZ ≅ Side: WX

 

4.

Using the AAS Theorem: http://www.mathopenref.com/congruentaas.html

Prove: ΔRPQ ≅ Δ QSR

Given: ∠PRQ ≅ ∠SQR

5.

Prove: Δ TQP ≅ Δ TRS

Given: Side: PT ≅ Side: ST

  • Using CPCTC: 

    Prove: ∠ Q ≅ ∠R

    Given: Side: PT ≅ Side: ST

Once you have completed the proofs on word you will create a bridge with toothpicks attached with glue. The bridge must have all triangles conruent to each other, must have at least  5 triangles. You will graded on overall neatness and congreuncy. Remember that the more triangles you do the more credit you get. 

Evaluation

Conclusion

In geometry many things have an actual use in the real world. In this case when using congruent triangles you can apply it to the world by making bridges, train tracks, and even our roof tops along with many more. This lesson was to extend your knowledge into reference more into depth how you can use congruent triangles in real life and not in a class room.

Credits

I am a student in geometry honors class. Making this Webquest has made me see how geometry is used daily in the real world and not just in a class room. It has given me a new point of view of math itself.

In this WebQuest you should have learned and understood congruent triangles and how to include them into real world problems. The hands on project was a demonstration of what many different types of triangles can be used for. Geometry is everywhere not just on paper and in the class room but all round you.