Geometry - Mini Similarity Book

Ms. Orr, Apr 22, 2020

Mini Similarity Workbook

Table of Contents

  1. General Definition of Similarity
    1. 1. Similarity Intro
    2. 2. Lamppost Similar Triangles Problem
  2. Similarity Minimum Conditions
    1. 1. AA Similarity Theorem
    2. 2. AA Similarity
    3. 3. SAS ~ Theorem
  3. Altitude to Hypotenuse
    1. 4. Why Similar Right Triangles?
    2. 5. Similar Right Triangles Animation
  4. Intro to Trigonometry
    1. Basic Right Angled Triangle Trig ratios
    2. Right Triangle Trig Practice-Finding Sides
    3. Right Trig Ratio
    4. Right Triangle Solver: Formative Assessment
    5. Right Triangle Trig: Solving for Sides (2)

1.

General Definition of Similarity

  • 1. 1. Similarity Intro
  • 2. 2. Lamppost Similar Triangles Problem

1.1.

1. Similarity Intro

[size=150][b]Two objects are similar if they are the same shape, but not necessarily the same size. [/b][/size][size=150][br][b][u][br][color=#ff0000]INSTRUCTIONS:[/color][/u] [/b]Move the sliders to transform the pink triangle in order to see if [math]\Delta[/math]CAT is similar to [math]\Delta[/math]DOG. It will be similar if you can rotate it, slide it and dilate it to match.[/size]
[size=150][b][color=#ff0000]QUESTION:[/color][br]Is [/b][math]\Delta[/math][b]CAT similar to [/b][math]\Delta[/math][b]DOG?[/b][/size]
– Ms. Orr

1.2.

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2.

Similarity Minimum Conditions

  • 1. 1. AA Similarity Theorem
  • 2. 2. AA Similarity
  • 3. 3. SAS ~ Theorem

2.1.

1. AA Similarity Theorem

[color=#000000]The [/color][b][color=#0000ff]AA Similarity Theorem[/color][/b][color=#000000] states:[/color][br][br][i][color=#0000ff]If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.  [/color][/i][br][br][color=#980000]Below is a visual that was designed to help you prove this theorem true in the case where both triangles have the same orientation.  (If the triangles had opposite orientations, you would have to first [b]reflect[/b] the white triangle [b]about any one of its sides[/b] first, and then proceed along with the steps taken in the applet.)  [/color][br][br][color=#000000]Feel free to move the locations of the [/color][color=#38761d][b]BIG GREN VERTICES[/b][/color][color=#000000] of either triangle before slowly dragging the slider. [/color][b] [/b][i][color=#ff0000]Pay careful attention to what happens as you do.[/color][/i]
Quick (Silent) Demo
– Ms. Orr, Tim Brzezinski

2.2.

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2.3.

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3.

Altitude to Hypotenuse

  • 1. 4. Why Similar Right Triangles?
  • 2. 5. Similar Right Triangles Animation

3.1.

4. Why Similar Right Triangles?

[color=#000000]Interact with the applet below for a few minutes, then answer the questions that follow.[/color]
Quick (Silent) Demo
– Ms. Orr, Tim Brzezinski

3.2.

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4.

Intro to Trigonometry

  • 1. Basic Right Angled Triangle Trig ratios
  • 2. Right Triangle Trig Practice-Finding Sides
  • 3. Right Trig Ratio
  • 4. Right Triangle Solver: Formative Assessment
  • 5. Right Triangle Trig: Solving for Sides (2)

4.1.

Basic Right Angled Triangle Trig ratios

– Peter22

4.2.

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4.3.

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4.4.

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4.5.

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