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Congruence Theorem Applet
The Congruence Theorem applet is an interactive tool that is designed primarily for high school level math, grades 9-12, with an emphasis coming in either 9th or 10th grade. The purpose of this applet is to get students to explore conditions that result in congruent triangles. Students start by selecting any three elements in the top right corner of the screen the applet is displayed in. The elements will then appear in the blue area of the screen. Students are then able to click and drag the elements to form a triangle. After the first triangle is formed, a new set of congruent elements will appear in the blue area of the screen. Students are expected to form another triangle with the new elements. Then, the students will be asked if the second triangle is congruent to the first one. They will be able to click and drag the second triangle over the first triangle to compare. If the two triangles are congruent, then the student will be asked to attempt make a third triangle that is not congruent to the original triangle.
Critique of Technology
How well does it work?
it correctly. Also, the program does not let you prove the SSS congruence theorem.
Are the written materials well organized and useful?
The instructions are very helpful. Before reading them, it is hard to grasp exactly how to arrange the elements to form a triangle. However, the instructions clearly outline how to operate the applet and what the objectives are.

Georgia Department of Education (2006). Mathematics Georgia Performance Standards. Retrieved from https://www.georgiastandards.org/standards/Georgia%20Performance%20Standards/Math-I-Stds.pdf
Georgia Department of Education (2011). Common Core Georgia Performance Standards CCGPS. Retrieved from https://www.georgiastandards.org/Common-Core/Documents/CCGPS-Gr9-12-Math-Standards.pdf
NCTM Illuminations. (n.d.). Retrieved from http://illuminations.nctm.org/ActivityDetail.aspx?ID=4%20

Congruence Theorem Applet
The Congruence Theorem applet is an interactive tool that is designed primarily for high school level math, grades 9-12, with an emphasis coming in either 9th or 10th grade. The purpose of this applet is to get students to explore conditions that result in congruent triangles. Students start by selecting any three elements in the top right corner of the screen the applet is displayed in. The elements will then appear in the blue area of the screen. Students are then able to click and drag the elements to form a triangle. After the first triangle is formed, a new set of congruent elements will appear in the blue area of the screen. Students are expected to form another triangle with the new elements. Then, the students will be asked if the second triangle is congruent to the first one. They will be able to click and drag the second triangle over the first triangle to compare. If the two triangles are congruent, then the student will be asked to attempt make a third triangle that is not congruent to the original triangle.

The Congruence Theorem applet does not require purchase of anything to use it. With that said, I would still recommend it for use in a classroom. However, if there was a fee to use the applet, then I would suggest finding a different app. Although it is useful, I do not believe it would be worth purchasing. That aside, there are many other applets available on the NCTM Illuminations website also. This applet, in particular, could benefit students when learning about congruence between triangles. It gives a visual representation of the different congruence axioms and students can also see which combination of elements does not result in congruence. However, I would recommend another applet for students to get a better grasp of the congruence axioms if there exists such an applet. This applet may distract from the concepts and ideas that the applet is designed to explore.
Activity
The following is a handout designed to explore the applet. Click here.
References
Common Core Georgia Performance Standards CCGPS (2011). Common Core State Standards For Mathematics. Retrieved from http://www.corestandards.org/assets/CCSS_Math%20Standards.pdf

Critique of Technology
How well does it work?
the program never actuallydoes not let you prove the SSS congruence theorem.
Are the written materials well organized and useful?
The instructions are very helpful. Before reading them, it is hard to grasp exactly how to arrange the elements to form a triangle. However, the instructions clearly outline how to operate the applet and what the objectives are.

Critique of Technology
How well does it work?
never actually
Are the written materials well organized and useful?
objectives are.
What are the purposes and goals for using this technology? Does the technology reach this goal?
The purpose of this applet is to get students to explore different conditions that result in congruent triangles. The goal is to broaden each student's understanding of congruence axioms such as SAS, ASA, and SSS. Students are given the opportunity to explore the different congruence axioms and are expected to make conjectures about which sets of elements result or do not result in congruent triangles. This applet accomplishes these goals. Students are able to explore different conditions and each set of conditions results in a new congruence theorem.
With this technology, students will broaden their knowledge and understanding of the different congruence axioms involving triangles. They will gain a better understanding of why each axiom holds while using a visual representation of each congruence axiom. Also, this applet can be used as an extension of teaching why some sets of elements do not result in congruence axioms, such as AAA. This tool may be used as a distinction between congruency and similarity between figures. However, any sort of discussions will have to be teacher led since the applet itself does not address these things. It only provides a visual representation.
Would you recommend this product for purchase to a school? Why or why not?
a classroom. ThereHowever, if there was a fee to use the applet, then I would suggest finding a different app. Although it is useful, I do not believe it would be worth purchasing. That aside, there are many to explore.
Activity
References

Critique of Technology
How well does it work?
it correctly. Also, the program never actually
Are the written materials well organized and useful?
objectives are.
What are the purposes and goals for using this technology? Does the technology reach this goal?
The purpose of this applet is to get students to explore different conditions that result in congruent triangles. The goal is to broaden each student's understanding of congruence axioms such as SAS, ASA, and SSS. Students are given the opportunity to explore the different congruence axioms and are expected to make conjectures about which sets of elements result or do not result in congruent triangles. This applet accomplishes these goals. Students are able to explore different conditions and each set of conditions results in a new congruence theorem.
With this technology, students will broaden their knowledge and understanding of the different congruence axioms involving triangles. They will gain a better understanding of why each axiom holds while using a visual representation of each congruence axiom. Also, this applet can be used as an extension of teaching why some sets of elements do not result in congruence axioms, such as AAA. This tool may be used as a distinction between congruency and similarity between figures. However, any sort of discussions will have to be teacher led since the applet itself does not address these things. It only provides a visual representation.
Would you recommend this product for purchase to a school? Why or why not?
in particular, wouldcould benefit students greatly when learning in congruence. However, I would recommend another applet for students to get a better grasp of the congruence axioms if there exists such an applet. This applet may distract from the concepts and ideas that the applet is designed to explore.
Activity
References

Congruence Theorem Applet
original triangle.
Below is a screen shot of the applet. Click here to access the applet.
{Congruence-Theorem.jpg}
The Congruence Theorem applet is a great interactive tool for students to explore the many different theorems dealing with congruent triangles. The options within the applet are very easy to understand and use. There are a few negatives however. One being that you must line up the elements exactly in order for them to "snap together." Also, it is unclear as to what elements work because it never says one does not work. You just have to realize it for yourself. This may be confusing to some students. They may believe they are doing it wrong when in fact they are doing it correctly.
Are the written materials well organized and useful?
objectives are.
What are the purposes and goals for using this technology? Does the technology reach this goal?
The purpose of this applet is to get students to explore different conditions that result in congruent triangles. The goal is to broaden each student's understanding of congruence axioms such as SAS, ASA, and SSS. Students are given the opportunity to explore the different congruence axioms and are expected to make conjectures about which sets of elements result or do not result in congruent triangles. This applet accomplishes these goals. Students are able to explore different conditions and each set of conditions results in a new congruence theorem.

Congruence Theorem Applet
asked to attempt make a original triangle.
Below is a screen shot of the applet. Click here to access the applet.
{Congruence-Theorem.jpg}
The Congruence Theorem applet is a great interactive tool for students to explore the many different theorems dealing with congruent triangles. The options within the applet are very easy to understand and use. There are a few negatives however. One being that you must line up the elements exactly in order for them to "snap together." Also, it is unclear as to what elements work because it never says one does not work. You just have to realize it for yourself. This may be confusing to some students. They may believe they are doing it wrong when in fact they are doing it correctly.
Are the written materials well organized and useful?
N/AThe instructions are very helpful. Before reading them, it is hard to grasp exactly how to arrange the elements to form a triangle. However, the instructions clearly outline how to operate the applet and what the objectives are.
What are the purposes and goals for using this technology? Does the technology reach this goal?
The purpose of this applet is to get students to explore different conditions that result in congruent triangles. The goal is to broaden each student's understanding of congruence axioms such as SAS, ASA, and SSS. Students are given the opportunity to explore the different congruence axioms and are expected to make conjectures about which sets of elements result or do not result in congruent triangles. This applet accomplishes these goals. Students are able to explore different conditions and each set of conditions results in a new congruence theorem.

Congruence Theorem Applet
The Congruence Theorem applet is an interactive tool that is designed primarily for high school level math, grades 9-12, with an emphasis coming in either 9th or 10th grade. The purpose of this applet is to get students to explore conditions that result in congruent triangles. Students start by selecting any three elements in the top right corner of the screen the applet is displayed in. The elements will then appear in the blue area of the screen. Students are then able to click and drag the elements to form a triangle. After the first triangle is formed, a new set of congruent elements will appear in the blue area of the screen. Students are expected to form another triangle with the new elements. Then, the students will be asked if the second triangle is congruent to the first one. They will be able to click and drag the second triangle over the first triangle to compare. If the two triangles are congruent, then the student will be asked to make a third triangle that is not congruent to the original triangle.