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Triangle Inequalities and Angle Relationships in Geometry Overview

Today's lesson in geometry focuses on understanding triangle angle-side inequalities and their constitutional properties. We'll begin with a warm-up problem to order angles from largest to smallest using inequalities. Practice will include analyzing given angles to classify triangle sides by length, measuring Australia’s coastline, and applying the triangle inequality theorem. Homework will consist of exercise assignments and a reflective journal on the week's learning and improvements. Clean-up and reminders will conclude our session.

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Triangle Inequalities and Angle Relationships in Geometry Overview

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Presentation Transcript

  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Check HW / Questions re Asgs #40-41? • Practice problem • Homework / Questions • Clean-up

  3. Warm-up problem: 1 min. • Write an inequality that puts the angles in order from largest to smallest:

  4. Practice:Triangle Angle-Side Inequalities Given that ∠CDB = 65°, ∠CBD = 72°, ∠ADB = 34°, and ∠A = 87°, list the segments in the diagram in order from longest to shortest.

  5. Distance Measurements 4100km Problem: Find the perimeter of Australia.

  6. Measuring the Coastline

  7. The Triangle Inequality • The lengths of any two sides of a triangle add up to at least as much as the length of the other. • In symbols: • For all triangles ABC, • AB + BC  AC, • AB + AC  BC, and • AC + BC  AB.

  8. The Triangle Inequality • The lengths of any two sides of a triangle add up to more than the length of the other. • In symbols: • For all triangles ABC, • AB + BC > AC, • AB + AC > BC, and • AC + BC > AB.

  9. Homework • Log 25 minutes: • Asgs #41-43 • Proof: • Prove Thm. 14 • “Test Problem” from portfolio • “Problems on Geometric Figures” questions • This week’s journal: • What work did you do this week? • What did you learn? • Review your portfolio and the comments in it.What improvements can you make based on it?

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

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