Write

1
Write

• What does it mean for two things to be similar?
• How is this different from two things being the
  same?
• Which idea is stronger? Why?
• How do you decide if two things are similar?

2
Recognizing Similarity

• Monday 7 April 2008

3
The Plan

• Today Recognizing similarity
• Tomorrow Proportion and right triangles
• Wednesday Finding similarities
• Thursday Similarity, area, and volume
• Friday Practice and an assessment

4
A quick warm-up
5
A Bad Riddle

• Why do maps have scales down in the corner?
• So they arent as big as the thing theyre
  mapping.

6
Scale Drawings

• To go from a map to real-life, we need to use a
  scale and cross multiplication.

7
Similarity

• Two objects are similar if you can map one onto
  the other using a scale factor.
• So the idea of a dilation is in play here.

8
Identifying Similarity

• We can tell two figures are similar if
• Corresponding angle measures are the same, or
• Corresponding side measures are the same.
• You only need one of these conditions to be true!

9
For Example
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Are these similar? Explain.
11
A Quick Thought Experiment

• Imagine an equilateral triangle.
• Now, cut it into four equilateral triangles.
• Now, get rid of the middle one, leaving you with
  three equilateral triangles.
• Cut each of those into four equilateral
  triangles.
• Now, get rid of the middle ones, leaving you with
  nine.
• Lather, rinse, repeat.

12
Self-Similarity the Sierpinski Gasket
13
Menger Sponge
14
Identifying Similarity

• We can tell two figures are similar if
• Corresponding angle measures are the same, or
• Corresponding side measures are the same.
• You only need one of these conditions to be true!