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Geometric Island Dwellings | Explore Equilateral Triangles

Today's plan includes understanding points, lines, and planes in geometry. Solve the Surfer and Spotter puzzles on an equilateral triangular island. Find the optimal house location to minimize distances. Homework instructions provided for further learning.

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Geometric Island Dwellings | Explore Equilateral Triangles

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Supplies Check / Pre-write • Two Problems: The Surfer and Spotter • Homework / Questions • Clean-up

  3. Supplies • Take out and be ready to show me… • compass • ruler • protractor • notebook/graph paper • 3 colors of pen or pencil • 2 composition books (or one plus a binder)

  4. Quick pre-write(Name, Date, Period @ top-right) • What do you know about… • …points? • …lines? • …line segments? • …planes? (Not the flying kind…) • If you know these words, tell what they mean: • collinear / noncollinear • coplanar / noncoplanar • concurrent • What shapes are formed by intersecting lines? • What about intersecting planes?

  5. Equilateral triangles • Take out • your notes • your equilateral triangle construction from yesterday

  6. The Surfer’s & Spotter’s puzzles Spotter: Wants access to all corners Surfer: Wants access to all sides

  7. The Island • Equilateral triangular island • 12km on each side

  8. The Spotter • Goal: • Choose a location for his house • Minimize the sum of the distances from the house to the vertices A, B, and C.

  9. The Spotter • Scale drawing of the island: 1cm = 1km • Example 1: • House at D • AD = 4.4km, DB = 9.1km, DC = 7.9km • Total distance: 21.4km • Example 2: • House at E • AE = 10.4km, EB = 5.1km, EC = 6.9km • Total distance: 22.4km.

  10. The Spotter • Using your triangle from yesterday or a new one (12cm on each side) as a model: • Choose several points on the island • For each point: • Measure the distance to each corner • Add up the distances. • What do you believe is the best place for the house? • …and how many km of path must the spotter clear? • What about the worst place? • …and how many km to clear from there?

  11. The Surfer • Goal: • Minimize the sum of the distances from his house to the sides of the island. • Note: • The shortest path from the house to a side is perpendicular to the side.

  12. The Surfer • Example. • This time you can measure them.

  13. The Surfer • Using your triangle from yesterday or a new one (12cm on each side) as a model: • Choose several points on the island • For each point: • Measure the distance to each side (again, perpendicular!) • Add up the distances. • What do you believe is the best place for the house? • …and how many km of path must the surfer clear? • What about the worst place? • …and how many km to clear from there?

  14. Homework • By Friday: Introduction email(subject: Period __ Geometry: Introduction) • Instructions on Schoology • Tonight: 10 minutes work on Khan Academy • Choose a topic you need to work on from the pre-test • Watch a video and work the associated problem(s)

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

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