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Geometry Class Plan: Area Theorems and Proofs

Today's geometry class focuses on reviewing homework related to area proofs and discussing theorems necessary for proving area calculations. The session will cover the area postulate and various area theorems for rectangles, squares, and triangles. Students will work in random groups to collaborate on problems and develop conjectures regarding area calculations. Homework includes working on proofs related to the area of a triangle, parallelogram, and trapezoid, as well as preparing materials for review in class.

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Geometry Class Plan: Area Theorems and Proofs

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Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review HW on Proofs; Questions? • Area Proof Work • Homework / Questions • Clean-up

  3. About Area 1 • We have: • the Area Postulate • the rectangle area postulate • the square area theorem • the right triangle area theorem • We want: • Area theorems for: • Maybe also theorems for: 2  A1 = A2 3 = = + 4 5 4 5

  4. Random Groups (1) • Ruth / Trevor • Atticus / Jade • Ally / Bridget • Keelan / Izzy • Callan / Celeste • Colton / Nathan / Jared

  5. Random Groups (2) • Graden / Shelton • Colby / Eva • Kai / Emily • Lucas / Kaitlyn • Sydney / Chester • Collin / Claire / Grace

  6. Random Groups (7) • Erin / Avery • Kesh / Nima • Megan / Sam / Olivia

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

  8. Homework • Take 20 minutes tonight to do this: • Work on proofs: • 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 = ???where b1 and b2are the bases and h is the altitude • Write down facts that might help prove/disprove your conjectures. • Log any conjectures you come up with; mark any conjectures that you prove. • Bring in what you’ve written and drawn, for me to check off in class.

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

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