Geometry Review

Stephanie Harman Smith, Feb 23, 2019

Table of Contents

  1. Vocabulary
    1. Animation 1
    2. Animation 3
    3. Animation 63
    4. Animation 81
    5. Animation 97
    6. Animation 134
    7. Animation 136
    8. Animation 137
    9. Proof Without Words
    10. Animation 98
    11. Animation 99
    12. Animation 100
    13. Animation 200
    14. Animation 173
    15. Animation 174
    16. Animation 103
    17. Animation 89
    18. Animation 12
    19. Animation 116
    20. Animation 50
    21. Animation 78
    22. Animation 76
    23. Animation 24
    24. Animation 96
    25. Animation 101
    26. Animation 33
    27. Animation 61
    28. Animation 45
    29. Animation 79
    30. Animation 88
    31. Animation 92
    32. Animation 91
    33. Animation 138
    34. Animation 225
    35. Animation 242
    36. Animation 243
  2. Vocabulary Quizzes
  3. Activities- Foundations
    1. Create a Triangle with Given Area: Quick Formative Assessment
    2. Create a Trapezoid with Given Area: Quick Formative Assessment
    3. Partition Line Segments
    4. Quiz: Distance in the Coordinate Plane (V1)
    5. Quiz: Distance in the Coordinate Plane (V2)
    6. Writing Equations of Parallel and Perpendicular Lines
    7. Perpendicular Lines Definition (& Consequence)
  4. Activities-Transformations
    1. Messing With Lisa
    2. Rotating Around Points: Ex. 17
    3. Reflecting About Lines: Ex. 18
    4. Translating by Vector: Ex. 16
    5. Reflections and Translations
    6. Composing Transformations: Ex. 20
    7. Exploring Dilations: Ex. 19
    8. Dilation Introduction: Transformers!
  5. Activities- Triangles
    1. Midsegments
    2. Orthocenter
    3. Centroid
    4. Incenter
    5. Circumcenter
    6. 3 Special Points!
  6. Activities- Trigonometry
    1. Practice: Pythagorean Theorem (1)
    2. Quiz: Pythagorean Theorem (2A)
    3. Right Triangles: Identifying Sides WRT Acute Angles
    4. Identifying Trig Ratios: Quick Formative Assessment
    5. Finding Exact Trig Ratios: Quiz Question Generator
    6. Finding Acute Angles of Right Triangles
    7. Right Triangle Trig: Solving for Sides
    8. Right Triangle Trig: Solving for Sides (2)
    9. Special Right Triangles: Basic Questions
    10. Quiz: Special Right Triangles
    11. Trigonometric Ratios (Right Triangle Context)
  7. Activities- Circles
    1. Equation & Graph of a Circle
    2. Circle Terminology
    3. Congruent Chords: Quick Investigation
    4. Diameters & Chords I (VA)
    5. Congruent Chords Action (A)
    6. Angle Formed by 2 Chords (II)
    7. Angles from Secants and Tangents (V1)
    8. Angle From 2 Secants (V2)
    9. Crossing Chords: Proof Hint
    10. Secants: Proof Hint
    11. 1 Radian: Clear Definition
    12. Movie: Radians to Revs
    13. Arc length: Quick Investigation
    14. Area of a Sector
    15. Arc Length and Area of a Sector (V1)
    16. Arc Length and Area of a Sector (V2)
    17. Radius Unwrapper v2.0
  8. Activities- Modeling
  9. Short Answer
    1. What "CO" in COsine Means
    2. Dilating a Line: HSG.SRT.A.1.A
    3. Dilating a Segment: HSG.SRT.A.1.B
  10. Honors
    1. Law of Sines (& Area)
    2. Law of Cosines: Discovery
    3. Medians & Equal Areas!
    4. Morley Action!
    5. Napoleon Motion!
    6. Hexagonal Napoleon Theorem?
    7. Viviani Action! (REVAMPED)
    8. Equal Triangular Areas in a Regular Pentagon
    9. NCTM Calendar Problem (11-2-2016)
    10. 9-Point Circle (Informal Investigation)
    11. Cut-The-Knot Action !!!
    12. Law of Sines (Illustrated)

1.

Vocabulary

  • 1. Animation 1
  • 2. Animation 3
  • 3. Animation 63
  • 4. Animation 81
  • 5. Animation 97
  • 6. Animation 134
  • 7. Animation 136
  • 8. Animation 137
  • 9. Proof Without Words
  • 10. Animation 98
  • 11. Animation 99
  • 12. Animation 100
  • 13. Animation 200
  • 14. Animation 173
  • 15. Animation 174
  • 16. Animation 103
  • 17. Animation 89
  • 18. Animation 12
  • 19. Animation 116
  • 20. Animation 50
  • 21. Animation 78
  • 22. Animation 76
  • 23. Animation 24
  • 24. Animation 96
  • 25. Animation 101
  • 26. Animation 33
  • 27. Animation 61
  • 28. Animation 45
  • 29. Animation 79
  • 30. Animation 88
  • 31. Animation 92
  • 32. Animation 91
  • 33. Animation 138
  • 34. Animation 225
  • 35. Animation 242
  • 36. Animation 243

1.1.

Animation 1

– Tim Brzezinski, Stephanie Harman Smith

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1.14.

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1.15.

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1.16.

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1.17.

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1.18.

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1.21.

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1.22.

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1.23.

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1.27.

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1.28.

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1.29.

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1.30.

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1.31.

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1.32.

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1.33.

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1.34.

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1.35.

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1.36.

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2.

Vocabulary Quizzes


    This chapter does not contain any resources yet.

3.

Activities- Foundations

  • 1. Create a Triangle with Given Area: Quick Formative Assessment
  • 2. Create a Trapezoid with Given Area: Quick Formative Assessment
  • 3. Partition Line Segments
  • 4. Quiz: Distance in the Coordinate Plane (V1)
  • 5. Quiz: Distance in the Coordinate Plane (V2)
  • 6. Writing Equations of Parallel and Perpendicular Lines
  • 7. Perpendicular Lines Definition (& Consequence)

3.1.

Create a Triangle with Given Area: Quick Formative Assessment

Quick (Silent) Demo
– Tim Brzezinski

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3.7.

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4.

Activities-Transformations

  • 1. Messing With Lisa
  • 2. Rotating Around Points: Ex. 17
  • 3. Reflecting About Lines: Ex. 18
  • 4. Translating by Vector: Ex. 16
  • 5. Reflections and Translations
  • 6. Composing Transformations: Ex. 20
  • 7. Exploring Dilations: Ex. 19
  • 8. Dilation Introduction: Transformers!

4.1.

Messing With Lisa

Note: LARGE POINTS are MOVEABLE.
– Tim Brzezinski

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5.

Activities- Triangles

  • 1. Midsegments
  • 2. Orthocenter
  • 3. Centroid
  • 4. Incenter
  • 5. Circumcenter
  • 6. 3 Special Points!

5.1.

Midsegments

– Stephanie Harman Smith

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6.

Activities- Trigonometry

  • 1. Practice: Pythagorean Theorem (1)
  • 2. Quiz: Pythagorean Theorem (2A)
  • 3. Right Triangles: Identifying Sides WRT Acute Angles
  • 4. Identifying Trig Ratios: Quick Formative Assessment
  • 5. Finding Exact Trig Ratios: Quiz Question Generator
  • 6. Finding Acute Angles of Right Triangles
  • 7. Right Triangle Trig: Solving for Sides
  • 8. Right Triangle Trig: Solving for Sides (2)
  • 9. Special Right Triangles: Basic Questions
  • 10. Quiz: Special Right Triangles
  • 11. Trigonometric Ratios (Right Triangle Context)

6.1.

Practice: Pythagorean Theorem (1)

– Tim Brzezinski

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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7.

Activities- Circles

  • 1. Equation & Graph of a Circle
  • 2. Circle Terminology
  • 3. Congruent Chords: Quick Investigation
  • 4. Diameters & Chords I (VA)
  • 5. Congruent Chords Action (A)
  • 6. Angle Formed by 2 Chords (II)
  • 7. Angles from Secants and Tangents (V1)
  • 8. Angle From 2 Secants (V2)
  • 9. Crossing Chords: Proof Hint
  • 10. Secants: Proof Hint
  • 11. 1 Radian: Clear Definition
  • 12. Movie: Radians to Revs
  • 13. Arc length: Quick Investigation
  • 14. Area of a Sector
  • 15. Arc Length and Area of a Sector (V1)
  • 16. Arc Length and Area of a Sector (V2)
  • 17. Radius Unwrapper v2.0

7.1.

Equation & Graph of a Circle

The following applet was designed to help you see the relationship between the equation of a circle and its graph. [br]Adjust the sliders "h", "k", and "r" (one at at time), and observe what happens to the graph and equation after altering each one. [br]Answer the questions below.
Questions:[br][br]1) What does the parameter "[color=#0a971e]h[/color]" in the equation of a circle tell you about the [i]graph of the circle itself[/i]? [br]2) What does the parameter "[color=#1551b5]k[/color]" in the equation of a circle tell you about the [i]graph of the circle itself[/i]? [br]3) What does the parameter "[color=#c51414]r[/color]" in the equation of a circle tell you about the [i]graph of the circle itself[/i]? [br]4) How is the value of "[color=#c51414]r[/color]" made evident in the equation?
– Tim Brzezinski

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8.

Activities- Modeling


    This chapter does not contain any resources yet.

9.

Short Answer

  • 1. What "CO" in COsine Means
  • 2. Dilating a Line: HSG.SRT.A.1.A
  • 3. Dilating a Segment: HSG.SRT.A.1.B

9.1.

What "CO" in COsine Means

[color=#000000]Take a few minutes to interact with the applet below.[br]Then, answer the questions that follow. [/color]
[color=#000000]In the right triangle above, what is the relationship between the [b][color=#1e84cc]blue angle[/color][/b] and [b][color=#ff00ff]pink angle[/color][/b]? [br](What vocabulary term/adjective describes the relationship between these 2 angles?) [/color]
[color=#000000]Fill in the blank with the correct word: [br][br]The _____________ of the [b][color=#1e84cc]blue angle[/color][/b] is the [b][color=#6aa84f]percentage displayed. [/color][/b][/color]
[color=#000000]Fill in the blank with the correct word: [br][br]The ___________________ of the [b][color=#ff00ff]pink angle[/color][/b] is the [b][color=#6aa84f]percentage displayed. [/color][/b][/color]
[color=#000000]Thus, we can conclude that if 2 angles are ______________________ (see your answer to (1)), then the __________ of [b][color=#1e84cc]one angle[/color][/b] is equal to the ____________________ of its [b][color=#ff00ff]___________________ [/color][/b]! [br][br]Notice how the first 2 letters of the last 2 blanks are the same? Why is this? [/color]
– Tim Brzezinski

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9.3.

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10.

Honors

  • 1. Law of Sines (& Area)
  • 2. Law of Cosines: Discovery
  • 3. Medians & Equal Areas!
  • 4. Morley Action!
  • 5. Napoleon Motion!
  • 6. Hexagonal Napoleon Theorem?
  • 7. Viviani Action! (REVAMPED)
  • 8. Equal Triangular Areas in a Regular Pentagon
  • 9. NCTM Calendar Problem (11-2-2016)
  • 10. 9-Point Circle (Informal Investigation)
  • 11. Cut-The-Knot Action !!!
  • 12. Law of Sines (Illustrated)

10.1.

Law of Sines (& Area)

Interact with the applet below for a minute. [br]Then, answer the questions that follow. [br](Please don't slide the 2nd slider until prompted to in the directions below.)
1) Take a look at the yellow right triangle on the left.[br]Write an equation that expresses the relationship among angle [i]B[/i], the triangle's height, and side [i]c[/i].
2) Rewrite this equation so that [i]height [/i]is written in terms of side [i]c[/i] and angle [i]B[/i].
3) Now consider the pink right triangle on the right. Write an equation that expresses the relationship among angle [i]C[/i], side [i]b[/i], and the triangle's height. [br]
4) Rewrite this equation so that [i]height[/i] is written in terms of side [i]b[/i] and angle [i]C[/i].
5) Take your responses to questions (2) and (4) to write a new equation that expresses the relationship among [i]C[/i], [i]B[/i], [i]c[/i], and [i]b[/i]. Write this equation so that [i]C[/i] and [i]c[/i] appear on one side of the equation and that [i]B[/i] and [i]b[/i] appear on the other.
6) Now drag the slider in the upper right hand corner. Now, given the fact that the length of segment [i]BC[/i] would be denoted as [i]a [/i](it's just not drawn in the applet above), write an expression for the area of this original triangle in terms of [i]a[/i], [i]b[/i], and [i]C[/i].
7) Same question as in (6) above, but this time write the area of the triangle in terms of [i]a[/i], [i]c[/i], and [i]B[/i].
8) Suppose that dragging the first slider dropped a height from point [i]C[/i] instead of point [i]A[/i]. Answer questions (1) - (5) again, this time letting [i]c[/i] serve as the base of this triangle (vs. side [i]a[/i]). Notice anything interesting in your results?
– Tim Brzezinski

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