Similarity

Arthur Lee, Martin McMulkin, Feb 1, 2018

Table of Contents

  1. Compare pictures, similar or non-similar
    1. Are they similar? (1)
    2. Are they similar? (2)
    3. Are they similar? (3)
    4. Are they similar? (4)
    5. Are they similar? (5)
    6. Are they similar? (6)
    7. Are they similar? (7)
    8. direction on map
  2. Study dilation
    1. tracing image of dilation
    2. dilation and similar triangles
    3. dilate and rotate
    4. a series of similar triangles
    5. radiation
    6. Pantograph with GeoGebra
  3. Combination of similar triangles
    1. Template for arranging two similar triangles
    2. make 2 similar triangles (1)
    3. make 2 similar triangles (2)
    4. make two overlapping triangles similar
    5. Find 2 similar triangles
  4. Other comparisons
    1. Rectilinear Figures
    2. side splitting quadrilateral
    3. compare shapes

1.

Compare pictures, similar or non-similar

  • 1. Are they similar? (1)
  • 2. Are they similar? (2)
  • 3. Are they similar? (3)
  • 4. Are they similar? (4)
  • 5. Are they similar? (5)
  • 6. Are they similar? (6)
  • 7. Are they similar? (7)
  • 8. direction on map

1.1.

Are they similar? (1)

Are these pictures similar?
The length and width of the rectangular pictures can be independently adjusted. [br]Make similar or non-similar pictures. [br]The individual scaling factors can be shown and its relation to similarity can be examined.
– 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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1.8.

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2.

Study dilation

  • 1. tracing image of dilation
  • 2. dilation and similar triangles
  • 3. dilate and rotate
  • 4. a series of similar triangles
  • 5. radiation
  • 6. Pantograph with GeoGebra

2.1.

tracing image of dilation

Drag B to make a sketch. You can right click each point to turn off tracing. Estimate how big the image is when tracing is off.
tracing image of dilation
– Arthur Lee

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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3.

Combination of similar triangles

  • 1. Template for arranging two similar triangles
  • 2. make 2 similar triangles (1)
  • 3. make 2 similar triangles (2)
  • 4. make two overlapping triangles similar
  • 5. Find 2 similar triangles

3.1.

Template for arranging two similar triangles

Two similar triangles
Template for arranging two similar triangles
– Arthur Lee

3.2.

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3.3.

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3.4.

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3.5.

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4.

Other comparisons

  • 1. Rectilinear Figures
  • 2. side splitting quadrilateral
  • 3. compare shapes

4.1.

Rectilinear Figures

Rectilinear figures that have equal corresponding angles but not proportional corresponding sides.
Rectilinear Figures
see http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/defVI1.html
– Arthur Lee

4.2.

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4.3.

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