Pythagorean Theorem

pythagorean theorem
The Pythagorean Theorem and its converse.
guzinta math pythagorean theorem

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pythagorean theorem

Students are introduced to the Pythagorean Theorem using an interactive demonstration of the proof of the theorem. Students explore the reasoning behind the proof, learn relevant parts of a right triangle, and then use the formula a2 + b2 = c2 to write lengths of hypotenuses of triangles given on the coordinate plane. Students end the module by determining integer c (hypotenuse) values given a and b values.

In the second module, students are introduced to the converse of the Pythagorean Theorem, which tells us that if a triangle has side lengths which satisfy a2 + b2 = c2, then it is a right triangle. Students are given triangles with various side lengths and use what they know about the converse to determine if the triangles are right triangles. Students then are briefly introduced to the extension of the Pythagorean theorem to 3 dimensions.

Finally, students practice solving a variety of common word problems which require the application of the formula a2 + b2 = c2 from the Pythagorean theorem. The final exercise introduces students to Pythagorean triples and asks them to write any three integers which are Pythagorean triples.

Module 2 Video

This video shows a proof of the Converse of the Pythagorean Theorem—taken from Euclid’s Elements (Proposition 48 of Book I). Pause the video after CD is drawn and elicit from students that it can be labeled with a since it is equal in length to BC. Pause the video again after DA is drawn and elicit from students that this side can be labeled as a2 + b2 and has the same length as AB.