Unit 8: Similarity

Jamie Nordstrom, Aug 16, 2017

Table of Contents

  1. 12.7 Dilations
    1. Properties of Dilations
    2. Dilation Introduction: Transformers!
    3. Dilating a Point (Intro)
    4. Dilating a Line: HSG.SRT.A.1.A
    5. Dilating a Segment: HSG.SRT.A.1.B
    6. Properties of Dilations
    7. Properties of Dilations (II)
  2. 7.6 Dilations and Similarity in the Coordinate Plane
  3. 7.1 Ratio and Proportion
  4. 7.2 Ratios in Similar Polygons
  5. 7.3 Triangle Similarity: AA, SSS, and SAS
    1. Angle -Angle: Triangle Investigation
    2. AA Similarity Theorem
    3. Proving Triangles Similar (1)
    4. Proving Triangles Similar (2)
    5. Proving Triangles Similar (3)
    6. Proving Triangles Similar (4)
    7. SAS ~ Theorem
    8. SSS ~ Theorem (V1)
  6. 7.4 Applying Properties of Similar Triangles
  7. 7.5 Using Proportional Relationships
    1. Parallel Lines Proportionality Theorem
    2. Parallel Lines Proportionality Theorem
  8. similar quadrilaterals
    1. SSSS: Similar Quads?
    2. AAA: Similar Quads?

1.

12.7 Dilations

  • 1. Properties of Dilations
  • 2. Dilation Introduction: Transformers!
  • 3. Dilating a Point (Intro)
  • 4. Dilating a Line: HSG.SRT.A.1.A
  • 5. Dilating a Segment: HSG.SRT.A.1.B
  • 6. Properties of Dilations
  • 7. Properties of Dilations (II)

1.1.

Properties of Dilations

This applet accompanies the [b]Introduction to Dilations[/b] activity given to you in class.  [br]Have fun with this!  
– Tim Brzezinski

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.

7.6 Dilations and Similarity in the Coordinate Plane


    This chapter does not contain any resources yet.

3.

7.1 Ratio and Proportion


    This chapter does not contain any resources yet.

4.

7.2 Ratios in Similar Polygons


    This chapter does not contain any resources yet.

5.

7.3 Triangle Similarity: AA, SSS, and SAS

  • 1. Angle -Angle: Triangle Investigation
  • 2. AA Similarity Theorem
  • 3. Proving Triangles Similar (1)
  • 4. Proving Triangles Similar (2)
  • 5. Proving Triangles Similar (3)
  • 6. Proving Triangles Similar (4)
  • 7. SAS ~ Theorem
  • 8. SSS ~ Theorem (V1)

5.1.

Angle -Angle: Triangle Investigation

[b]Students:[br][/b][br]Please use the GeoGebra task applet below to complete the [b]Angle-Angle (Investigation) [/b]given to you at the beginning of class. [br][br][b]LINK:[/b] [b][color=#0000ff][url=https://docs.google.com/document/d/10gizSV-6UM_E6amlcEYLmVmnWgqpW_jWti6MYAyoSwk/edit?usp=sharing]Angle-Angle (Investigation)[/url][/color] [/b]
– Tim Brzezinski

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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6.

7.4 Applying Properties of Similar Triangles


    This chapter does not contain any resources yet.

7.

7.5 Using Proportional Relationships

  • 1. Parallel Lines Proportionality Theorem
  • 2. Parallel Lines Proportionality Theorem

7.1.

Parallel Lines Proportionality Theorem

[color=#000000]This applet accompanies the [/color][color=#0000ff][b]Parallel Lines Proportionality Theorems [/b]activity worksheet[/color][color=#000000] given to you at the beginning of class. [br][br][/color][b][color=#000000]Teachers: [/color][/b][b][color=#cc0000]A PDF copy of this lesson activity can be found below the applet. [/color][/b]
Parallel Lines Proportionality Theorem
– Tim Brzezinski

7.2.

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8.

similar quadrilaterals

  • 1. SSSS: Similar Quads?
  • 2. AAA: Similar Quads?

8.1.

SSSS: Similar Quads?

[color=#000000]Recall that the SSS Triangle Similarity Theorem states that if all 3 sides of one triangle are in proportion to all 3 sides of another triangle, then those triangles are similar. (For an informal proof of this theorem, go to [/color][color=#000000]https://tube.geogebra.org/m/yKFwXvRj). [br][br][/color][color=#0000ff][i]Yet does the same hold true for quadrilaterals? That is, if all 4 sides of one quadrilateral are in proportion to all 4 sides of another quadrilateral, can we claim that those two quadrilaterals are similar? [/i][/color][color=#000000] [br][br][/color][color=#0000ff][i]Since congruence of polygons is a special case of similarity of polygons (where the scale factor = 1), can we conclude that if 4 sides of one quadrilateral are congruent to 4 sides of another quadrilateral, then those quadrilaterals are congruent? (In essence, if the SSS Theorem proves triangles congruent, is there such an "SSSS Theorem" that proves 2 quadrilaterals congruent?) [/i][/color][color=#000000][br][br][/color][color=#980000]Interact with the applet below and respond to these questions. [/color]
– Tim Brzezinski

8.2.

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