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!
★Selected Answers in pdf form.
★Selected Answers online, password protected. For students to correct at home!
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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About Courage To Core:
We all have an innate curiosity about how the world works. We are wired to experiment at the edges of our knowledge, to look for patterns and to draw conclusions. Mistakes are the welcome surprises which help us refine the experiment. In a student-centered classroom, students collaborate to ask questions, gather data, interpret results and articulate understanding. Success at the edge of knowledge demands persistence and creativity. Courage To Core provides a context for students to work together to become the agents of their success and the owners of their cognition. If you like Courage To Core, please give me a positive rating to help me get started on TpT! You get credits towards future TpT purchases with every rating you give! Just revisit the purchased item in my store and scroll down to star me! Thanks!