# Proving the Pythagorean Theorem with Similar Triangles

Subject
Resource Type
Common Core Standards
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4.0
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Compressed Zip File

768 KB|17 pages
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Product Description
Students will develop the Altitude to Hypotenuse Theorems and the Pythagorean Theorem with carefully guided proofs. The Take-home Message: The Pythagorean Theorem can be proven by observing that an altitude to the hypotenuse creates 3 similar triangles. Two of the resulting proportions can be combined then simplified to give us the Pythagorean Theorem. This mission is aligned with Common Core State Standards: HSG.SRT.B.4, HST.SRT.B.5.

The fun stuff:
Proving the Pythagorean Theorem through similarity is a far-reaching and satisfying journey involving proportionality, visualization and proof. An intellectually satisfying yet wholly accessible experience!

The zip file includes:
★The mission. (10 pages).
★A two-page Quick Start guide for teachers. Detailed and helpful!

The mission includes:
•A review of dilation, similarity and applications of the Pythagorean Theorem.
•Geometric means and reflected and rotated triangles which are similar to each other.
•Proof of the Altitude to Hypotenuse Theorems.
•Proof of the Pythagorean Theorem.
•Problems requiring both theorems.

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Total Pages
17 pages
Included
Teaching Duration
2 days
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\$3.00