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Geometry Lesson on Triangle Area Theorem and Proofs

Today’s geometry lesson focuses on the Area Theorem for triangles. We will greet the class, review homework on the general triangle area theorem, and discuss how to find the area of a triangle. Students will state the theorem, set up a proof, and log any conjectures. A cube dissection puzzle will challenge students' understanding. We’ll conclude with Khan Academy recommendations for practice on area proofs, including formulas for triangles, parallelograms, and trapezoids. Please remember to clean up your spaces at the end of class!

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Geometry Lesson on Triangle Area Theorem and Proofs

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review HW: General Triangle Area Theorem • Lesson: Area Proofs • Homework / Questions • Clean-up

  3. Review • Homework included: • Tell how to find the area of a triangle. • State that formula as a theorem, and add it to your conjectures log. • Set up the proof for it, and think about how you might prove it. • Log any other conjectures you come up with. • Bring in what you’ve written and drawn, for me to check off in class. • Find a partner. Discuss how you stated the theorem. • What is given? What is the goal?

  4. Puzzle: Cube DissectionProgress? 3” x 3” wooden cube  twenty-seven 1” x 1” cubes Possible with fewer than six cuts?

  5. Homework • 25+ minutes: • Khan Academy recommendations • Practice with area proofs

  6. Area Formulas • Area of a triangle = ½ bhwhere b is any side and h is the altitude to that side • Area of a parallelogram = bhwhere b is any side and h is the altitude to that side • Area of a trapezoid = ½(b1 + b2)hwhere b1 and b2 are the bases and h is the altitude

  7. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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