Geometry Grade 8

Jessica Lampert, Nov 10, 2017

transformation reflection translation rotation dilation similar congruent

Table of Contents

  1. ReFLect (Flip)
    1. ReFLections (Flip)
    2. Transformation: Reflection
  2. RoTate (Turn)
    1. RoTation (Turn)
    2. 'Tangram' Puzzle 'Cat'
    3. Rotating a Triangle Around a Coordinate Axis
  3. TranSLate (Slide)
    1. TranSLation (SLide)
    2. Translating Triangle by a Vector
  4. Dilate (Reduce or Enlarge)
    1. Dilation (Reduce or Enlarge)
    2. Dilation Introduction: Transformers!
    3. Properties of Dilations
    4. Rotational and Reflection Symmetry
    5. Dilating a Segment: HSG.SRT.A.1.B
    6. Dilating a Line: HSG.SRT.A.1.A
  5. Composite Transformations
    1. Reflections, Rotations, Dilations, and Translations
    2. 'Tangram' Puzzle 'Cat'
    3. Double Reflection of an object
    4. Two Reflections
    5. Translating and Rotating
  6. Transformations with lines, line segments, angles, and parallel lines
    1. Transformations of Parallel line segments
    2. Messing With Lisa
    3. Rotational and Reflection Symmetry
    4. Geometric Transformations
  7. AA Similarity
    1. AA Similarity Theorem
    2. Triangle Similarity Criteria - AA
  8. Parallel lines cut by a transversal
    1. Parallel Lines Cut by a Transversal
    2. Transversal Intersects Parallel Lines

1.

ReFLect (Flip)

  • 1. ReFLections (Flip)
  • 2. Transformation: Reflection

1.1.

ReFLections (Flip)

Click on the black line of symmetry and drag it to reflect the figure over the line of symmetry. Is the image similar on congruent?
[size=200]Is the image [b]similar [/b]or [b]congruent [/b]to the preimage?[/size]
– Dtravis2, Jessica Lampert

1.2.

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2.

RoTate (Turn)

  • 1. RoTation (Turn)
  • 2. 'Tangram' Puzzle 'Cat'
  • 3. Rotating a Triangle Around a Coordinate Axis

2.1.

RoTation (Turn)

Move the [color=#ff0000][u][b]red[/b][/u] [/color]point to change the angle of rotation.[br]Move points E,F,G, and H to see how that effects the image.[br][br]Is the image similar or congruent to the preimage?
[size=150][size=200]Is the image [b]similar [/b]or [b]congruent[/b] to the preimage?[/size][/size]
– Jessica Lampert, Dtravis2

2.2.

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2.3.

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3.

TranSLate (Slide)

  • 1. TranSLation (SLide)
  • 2. Translating Triangle by a Vector

3.1.

TranSLation (SLide)

Click on the box to show the image of the figure after a translation. Slide the sliders to translate the figure up, down, right, and left. Is the image similar or congruent?
[size=200]Is the image [b]similar [/b]or[b] congruent[/b] to the preimage?[/size]
– Dtravis2, David Travis, Jessica Lampert

3.2.

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4.

Dilate (Reduce or Enlarge)

  • 1. Dilation (Reduce or Enlarge)
  • 2. Dilation Introduction: Transformers!
  • 3. Properties of Dilations
  • 4. Rotational and Reflection Symmetry
  • 5. Dilating a Segment: HSG.SRT.A.1.B
  • 6. Dilating a Line: HSG.SRT.A.1.A

4.1.

Dilation (Reduce or Enlarge)

Adjust the scale factor [b]k[/b]. How does this effect the image?[br]Move points A, B, C, and D. How does this effect the image?
[size=200]Is the image [b]similar[/b] or[b] congruent[/b] to the preimage?[/size]
– Jessica Lampert, Dtravis2

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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5.

Composite Transformations

  • 1. Reflections, Rotations, Dilations, and Translations
  • 2. 'Tangram' Puzzle 'Cat'
  • 3. Double Reflection of an object
  • 4. Two Reflections
  • 5. Translating and Rotating

5.1.

Reflections, Rotations, Dilations, and Translations

Drag each slider to observe the transformations individually or click the play button to observe all at the same time.
– vitullo

5.2.

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5.3.

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5.4.

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5.5.

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6.

Transformations with lines, line segments, angles, and parallel lines

Transformations with lines, line segments, angles, and parallel lines

  • 1. Transformations of Parallel line segments
  • 2. Messing With Lisa
  • 3. Rotational and Reflection Symmetry
  • 4. Geometric Transformations

6.1.

Transformations of Parallel line segments

[size=200]Click on the [b]REFLECT [/b]box.[br]Are the images of the segments congruent?[/size]
[size=200]Click on the [b]ROTATE [/b]box.[br]Are the images of the segments congruent?[/size]
C
[size=200]Click on the [b]TRANSLATE [/b]box.[br]Are the images of the segments congruent?[/size]
Click on
[size=200]Click on the [b]DILATE [/b]box.[br]Are the images of the segments congruent?[/size]
– Jessica Lampert

6.2.

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6.3.

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6.4.

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7.

AA Similarity

  • 1. AA Similarity Theorem
  • 2. Triangle Similarity Criteria - AA

7.1.

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
– Tim Brzezinski

7.2.

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8.

Parallel lines cut by a transversal

  • 1. Parallel Lines Cut by a Transversal
  • 2. Transversal Intersects Parallel Lines

8.1.

Parallel Lines Cut by a Transversal

Move points A, B, C.
– Terry Lee Lindenmuth

8.2.

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