## Learners

This WebQuest is designed for 10th-12th grade Geometry students in their second semester, studying triangle relationships. Students will have previous knowledge about basic and complex proof formats, especially those involving triangles and their relationships.

## Educational Goal

This WebQuest will be used at the beginning of an extension unit for triangles, where students will study the special relationships among right triangles and their properties. Students will explore and learn about several proofs for the Pythagorean Theorem and construct their own right triangle relationships using multiple examples. Following the WebQuest, students will be familiar with several ways to construct a proof for the Pythagorean Theorem, as well as be able to give background knowledge about the work of Pythagoras. They will apply what they have learned in their future work with right triangles and use this exploration as a stepping block to exploring other right triangle relationships in subsequent sections of their textbook.

## Standards Addressed (according to Michigan HSCEs)

G.1.2.3 Know a proof of the Pythagorean Theorem, and use the Pythagorean Theorem and its converse to solve multi-step problems. (This standard will be the focus of the WebQuest)

G1.1.1 Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles, and right angles.

G1.1.2 Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles.

G1.1.1 Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles, and right angles.

G1.1.2 Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles.

## Process

Students will be given an introduction to Pythagoras as a mathematician and will recording information about what they’ve learned through the reading before moving on to the rest of the Quest. Students will explore a number of ways the Pythagorean Theorem can be proven through the work of others. Methods of proof will be located on various websites—some of which are interactive—and in the student textbook. They will keep a log of their work in their class notebooks, as the proofs lend themselves well to student activity. After students have explored each proof of the theorem, students will apply the theorem to solving multiple real-life problems involving right triangles and distance measurement, including one exploration using structures around the world. Students will decide which proof they felt demonstrated the theorem the best and share the explanation with the class through a short presentation.

## Resources

Prior to using this WebQuest in class, students will be reminded of what the theorem says and how it is used in basic geometry. The class will discuss how the theorem may be useful in the world and read one explanation of where the theorem began in, “What’s Your Angle, Pythagoras?” (a children’s book by Julie Ellis). Materials needed: class notebooks (each student has one for record of work), graph paper (for completing proof in textbook, pg 416), colored paper (several sheets for each student), graphing calculator (or basic calculator with square root capabilities), Prentice Hall

*Geometry, Michigan Edition*(optional – instructions needed also found in online document). Each student will need access to a computer with internet (or students may work in pairs if needed). Students will need access to the websites listed in the credits below.## Credits

This WebQuest is the origninal work of Courtney Mills, teacher at Baldwin High School, in Baldwin, MI. It could not be completed, however, without the use of the following resources:

~For Pythagoras cartoon used on opening slide,

http://satoss.uni.lu/members/sasa/teaching/Math356/CourseDiary/cd614.php

~For Task 3.1 exploration directions and “How far can you see?” project directions (Task 6)and set up,

~Additional websites accessed throughout,

http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

http://www.notablebiographies.com/Pu-Ro/Pythagoras.html

http://www.mathopenref.com/pythagoras.html

http://math.ucr.edu/~jdp/Relativity/Pythagorus.html

http://www.mathsisfun.com/geometry/pythagorean-theorem-proof.html

http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html

http://www.math.hmc.edu/funfacts/ffiles/10007.2.shtml

http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/Pythagorean.html

http://www.pbs.org/wgbh/nova/proof/puzzle/use.html

http://www.tallestskyscrapers.info/images/tallest-buildings.jpg

http://architecture.about.com/library/bltall.htm

~For Pythagoras cartoon used on opening slide,

http://satoss.uni.lu/members/sasa/teaching/Math356/CourseDiary/cd614.php

~For Task 3.1 exploration directions and “How far can you see?” project directions (Task 6)and set up,

*Geometry, Michigan Edition.*Prentice Hall. 2008. p. 416, 463.~Additional websites accessed throughout,

http://www.historyforkids.org/learn/greeks/science/math/pythagoras.htm

http://www.notablebiographies.com/Pu-Ro/Pythagoras.html

http://www.mathopenref.com/pythagoras.html

http://math.ucr.edu/~jdp/Relativity/Pythagorus.html

http://www.mathsisfun.com/geometry/pythagorean-theorem-proof.html

http://www.pbs.org/wgbh/nova/proof/puzzle/theorem.html

http://www.math.hmc.edu/funfacts/ffiles/10007.2.shtml

http://jwilson.coe.uga.edu/EMT668/emt668.student.folders/HeadAngela/essay1/Pythagorean.html

http://www.pbs.org/wgbh/nova/proof/puzzle/use.html

http://www.tallestskyscrapers.info/images/tallest-buildings.jpg

http://architecture.about.com/library/bltall.htm