Congruent Triangles

You have been oriented on the different concept used in geometry. can you still distinguished definition from property? What about property from postulate? Postulate from theorem? They all seem the same in your normal English subject but in math one is different to another.You have been oriented on the different concept used in geometry. can you still distinguished definition from property? What about property from postulate? Postulate from theorem? They all seem the same in your normal English subject but in math one is different to another. They may differ in meaning and standards but all of them are used to prove that two triangles are congruent.

Given the below is a link to picture. The picture is an example of symmetric worlds or simple congruent image. Click the link to view the picture. (https://congruenttrianglesforjammy.blogspot.com/2019/10/the-said-picture-ispresented-below.html)

Congruent and similarity are different form each other. When your mother asked you to buy two heads of garlic, your mother is referring to one object which is the garlic. Frankly speaking the two heads of garlic are the same but are they congruent? They might be or they might be not. Another head might have ten cloves and the other might have six cloves. The question is how do you prove it?

Same goes for two triangles. They are both triangles but how do you prove that they are congruent. Right at this moment, the definitions, postulates, properties and theorem comes to the picture. Their role in mathematics is to prove that something is always or sometimes true.

On this web quest our main focus is to use them to prove that two triangles are congruent. Before proceeding make sure that you have your copies of definitions, properties, postulates, common notion and theorems/propositions.

There are different methods on how you can prove that two triangles are congruent. This link (https://congruenttrianglesforjammy.blogspot.com/2019/10/methods-of-proving.html) provided at least seven methods of proving. Make sure to read them. 

Another thing that you should make sure to know of are the postulates that are used in proving congruence of two triangles. Click on this site to know them. (https://congruenttrianglesforjammy.blogspot.com/2019/10/postulates-in-proving-triangle-congruent.html)

In this web quest, you will explore the different concept in math to prove the congruence of two triangles. Three links are given and among those links, I would like to ask each student to pick out two.However, before you move on you have to learn first the different methods of proving and the different postulates used in proving the congruence of two triangles. Make sure that you have read it before proceeding. The links are at the introduction of this web quest.

After reading the two links and you still have a rough idea on how to prove and what are the postulates , I recommend that you further read on those topic. You can also read this site (https://www.mathsisfun.com/geometry/triangles-congruent.html ) for further knowledge. 

The task is to be done individually. Remember to only choose two sites. Good luck!

You are now on the process stage wherein you'll apply what you've read form the previous stages. 

The activity is to be done individually. Here are the steps that you need to follow:

1. From the given five links, choose two links that will be your activity.
2. After so, open the Microsoft word where you’ll copy the format of the link.
3. Plan on how you will prove the following given. Make sure that your proving is continuous. Do not prove another statement without linking it to your previous statement.
4. After answering, save your document then name it using your name. Example: Jamela Fabianes.doc
5. Lastly, email your work at fabianesjamelajoy@gmail.com. I will only accept until Friday noon. You have a week to finish the task.

 Remember to choose only two!

      1. https://congruenttrianglesforjammy.blogspot.com/2019/10/prove-1.html

       2. https://congruenttrianglesforjammy.blogspot.com/2019/10/prove-2.html

       3. https://congruenttrianglesforjammy.blogspot.com/2019/10/prove-3.html

There are going to be two process on how we’ll evaluate your answers.

First, after passing your answers to my email, I will email your scores on your work. your work will be evaluated in terms of continuous proving, complete proving and the relevance of your proving.

Continuous proving will be given 15 points. This stands for the step by step process of your proving. The continuousness of your proving will answer the question, “Is my prove in number 1 related to my prove in number 2?”

Complete Proving will be given 20 points. This determines if you included all the necessary proving in your table of proof. Skipping and magic is not accepted in this area.

Relevance of your proving will be given 15 points. This determines how understandable your proof is to me. This is not a subjective type of question where in any answer will do. For every given proving exercises, remember that there is only one table of proof for each.

Second is you print your answers and let your classmates evaluate your work. you can also evaluate his work. discuss on what are the things that  you do not understand and what you found wrong on each other’s work.

Hopefully you learned a lot from this quest. As you can see, in this quest you’ve learn the methods of proving and the instruments used on how to prove two triangles are congruent. You also learn the interconnection of the properties, propositions, common notions, postulates and definitions. Remember that in Mathematics, we move on but we do not forget. We always carry our previous lesson to our current lesson. Hope you’ll learn to apply this to your life.

References:

https://www.mathsisfun.com/geometry/triangles-congruent.html

Buasen, J. M. (n.d.). Plane Geometry.

Geogebra App

On this web quest, you'll simply learn how to prove that two triangles are congruent. That includes the methods and the instruments used in proving such. The interconnection of all the statements in the mathematics world is also used in this web quest.

In checking the work of the students on this kind of activities, it is wise if you check three main things : continuous, completeness, and relevance of the proofs. This topic is just the start of the proving path, it good if you let your students master this topic before moving on.