Proving Pythagoras' Theorem

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SWBAT prove the Pythagorean Theorem using similar triangles.

Big Idea

Students will first explore similarity relationships between triangles and then will in a step by step checklist, prove the Pythagorean Theorem using similar triangles.

Do Now

10 minutes

Exploration of Similar Triangles

25 minutes

Proving Pythagorean Theorem

30 minutes

In this section of class notes, students will go through an 11-step checklist to prove the Pythagorean Theorem using similar triangles. This proof requires students to persevere through a very challenging application of similar triangles (MP 1) and reason abstractly by using variables to represent lengths of sides (MP 2).

The video explanation of this proof is available through Khan's Academy, and can be a great resource for teachers to use to review. 

After going through the entire proof in a check-list format, I then like to show the Khan Academy video starting at minute 4. 

This helps students to see the entire proof in one clear explanation.  If your students seem to really understand the proof, you can skip the video and ask for a student or group of students to talk through the proof again for the class. 

Activity/Homework and Exit Ticket

15 minutes

The Activity-Homework for this lesson asks students to watch a the video below explaining President James Garfield's proof of Pythagorean Theorem.  This would be a great assignment to do in class, if time remains or to have students work on independently if you have access to a computer lab.  You could easily extend this activity by asking students to watch a third video on a proof of Pythagorean Theorem.  You may want to ask students to consider why there are so many proofs for this particular theorem.

The exit ticket for this homework asks students to turn and talk to a partner.  Students can walk through the check-list proof done in today's class and summarize this for each other.  You can also ask one student to review or talk through the proof, if time remains. 


President Garfield's Proof