Isosceland

Arthur Lee, Nov 12, 2022

Isosceland

Table of Contents

  1. Mission Isosceles
    1. Make an isosceles triangle
    2. Hinging Triangles
    3. Another hinging triangles
    4. a triangle ABC cut into 2
    5. another triangle ABC cut into 2
    6. find the angles
    7. Langley Problem
  2. Isosceles Hunt
    1. isosceles hunt 1
    2. isosceles hunt 2
    3. isosceles hunt 3
  3. Anatomy
    1. bisector of a triangle
    2. triangle fold
  4. A special isosceles triangle
    1. doubling and halving a triangle
    2. Simple Tangram
    3. PMC 2014-15 Q6
    4. PMC 2012-13 Q4

1.

Mission Isosceles

  • 1. Make an isosceles triangle
  • 2. Hinging Triangles
  • 3. Another hinging triangles
  • 4. a triangle ABC cut into 2
  • 5. another triangle ABC cut into 2
  • 6. find the angles
  • 7. Langley Problem

1.1.

Make an isosceles triangle

Drag the point C to make an isosceles triangle.
In your triangle, which sides are equal?
Do you see any equal angles in your triangle? Which ones?
– Arthur Lee

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Isosceles Hunt

  • 1. isosceles hunt 1
  • 2. isosceles hunt 2
  • 3. isosceles hunt 3

2.1.

isosceles hunt 1

[list][*]How many isosceles triangles do you see? [br][/*][*]Which triangles are isosceles? How do you know?[br][/*][*]Which segments are equal?[/*][*]Which angles can you find?[/*][*]If you can move A,B,C,D, can you make more isosceles triangles in this figure?[/*][/list]
If you prefer a more accurate figure or a moving one, try the following.[br](Teacher may move this figure to another page as a separate section of this task.)
Use the following note for your rough work or sharing.
Go to Isosceles Hunt 2:[br]https://www.geogebra.org/m/rwdgb4ez
– Arthur Lee

2.2.

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2.3.

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3.

Anatomy

  • 1. bisector of a triangle
  • 2. triangle fold

3.1.

bisector of a triangle

A line is drawn to pass through the vertex A and cut its opposite side. Drag D to make this line:[br]1. bisect the angle at A;[br]2. bisect the side BC;[br]3. cut BC perpendicularly.[br]Can we make 2 (but not 3) of these conditions true?
– Arthur Lee

3.2.

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4.

A special isosceles triangle

  • 1. doubling and halving a triangle
  • 2. Simple Tangram
  • 3. PMC 2014-15 Q6
  • 4. PMC 2012-13 Q4

4.1.

doubling and halving a triangle

doubling and halving an isosceles right triangle for exploring powers of 2
Try to zoom in and out when changing the size of the triangles:[br][url=https://youtu.be/SHv3bktJL7I]https://youtu.be/SHv3bktJL7I[/url] [br][br]There is a similar applet based on a rectangle:[br][url=https://ggbm.at/FQ8f4RPm]https://ggbm.at/FQ8f4RPm[/url][br]
– Arthur Lee

4.2.

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4.3.

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4.4.

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