Hart Interactive

Ulli Skillman, Mar 4, 2016

Resources to use with the Hart Interactive Text

Table of Contents

  1. Constructions
  2. Transformations
    1. L5 Circumcenter
    2. Messing With Lisa
    3. Escherized Tessellation
    4. Forest Hills (8.G.3 Describe the effect of dilations, trans)
    5. Composition of dilations
  3. Similarity
    1. Definition of Similarity 1
    2. Definition of Similarity 2
    3. Definition of Similarity 3
    4. Definition of Similarity 4
    5. Similar Game (Level 1)
    6. Dilation Exploration
    7. Similar Game (Level 2)
    8. Similar Game (Level 3)
    9. Parallel Line Side Splitter Theorem (Corollary)
    10. Dilations Practice
    11. Side Splitter Exploration
    12. Similar Figures: Dynamic Illustration
    13. AA Similarity Theorem
    14. Similar Triangles
  4. Trigonometry
    1. Sine and Cosine of Complementary angles
    2. Pythagorean Theorem Proof without Words
    3. Right Triangle vs. Acute & Otuse Trianlges
  5. Quadrilaterals
    1. Parallelogram 2
    2. Parallelogram Practice
  6. Area and Volume
    1. Cavalieri's Principle
    2. Principle of Parallel Slices in the Coordinate Plane
    3. Cavalieri's Principle
    4. Trisecting a Rectangular Prism (Improved)
    5. Square Cross Section: Finished Product
    6. right triangle paradox
  7. Coordinate Geometry
    1. Module 4 Lesson 1
    2. Proportional Segments Using Ratios
  8. Circles
    1. M5L2 1. Diameter and Chord
    2. M5L2 2.A. Congruent Chords
    3. M5L2 2.B. Equidistant Chords
    4. M5L2 3. Congruent Chords and Central Angles
    5. Inscribed Angle Demonstration
    6. Inscribed Quadrilateral
    7. M5 L11/12 Properties of Tangents (A)
    8. Properties of Tangents Drawn to Circles (B)
    9. Tangents, Secants and Central Angles
    10. Tangent-Secant angle at Radius
    11. M5 L14
    12. Angles and arcs of secant lines intersecting a circle
    13. Tangents to Circles: Investigation
    14. Tangent to Circle: Construction 1
    15. Lesson 9.2 Chord Properties 1
    16. ACCESS - Circles and Central Angles 1
    17. Parallel Lines and Intercepted Arcs
    18. Angles Outside Circle Theorems
    19. L17 Two Intersecting Chords in a Circle
    20. Two Intersecting Chords in a Circle
    21. Relationships of segment lengths from the intersection of secants, chords, and tangents of a circle
    22. Chords intersecting outside the circle
    23. ACCESS - Secants
    24. ACCESS - Secants and Tangents

1.

Constructions


    This chapter does not contain any resources yet.

2.

Transformations

  • 1. L5 Circumcenter
  • 2. Messing With Lisa
  • 3. Escherized Tessellation
  • 4. Forest Hills (8.G.3 Describe the effect of dilations, trans)
  • 5. Composition of dilations

2.1.

L5 Circumcenter
– Ulli Skillman

2.2.

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2.3.

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2.4.

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2.5.

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3.

Similarity

  • 1. Definition of Similarity 1
  • 2. Definition of Similarity 2
  • 3. Definition of Similarity 3
  • 4. Definition of Similarity 4
  • 5. Similar Game (Level 1)
  • 6. Dilation Exploration
  • 7. Similar Game (Level 2)
  • 8. Similar Game (Level 3)
  • 9. Parallel Line Side Splitter Theorem (Corollary)
  • 10. Dilations Practice
  • 11. Side Splitter Exploration
  • 12. Similar Figures: Dynamic Illustration
  • 13. AA Similarity Theorem
  • 14. Similar Triangles

3.1.

Definition of Similarity 1

G-SRT.2 Practice using the definition of similarity in terms of similarity transformations to decide if two figures are similar.

Are the figures similar?
– Jamie Peters

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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4.

Trigonometry

  • 1. Sine and Cosine of Complementary angles
  • 2. Pythagorean Theorem Proof without Words
  • 3. Right Triangle vs. Acute & Otuse Trianlges

4.1.

Sine and Cosine of Complementary angles

Exploration of Sine and [b]Co[/b]sine of [b]co[/b]mplementary angles (Adapted from work by tohweeteck on GeogebraTube)

What is the complement of a 35 degree angle? Click on Sin Theta Click on Complementary angle Click on Sin (90 - theta) Click on Cos(90- theta) Change theta to 25 degrees and look at the values What conjecture can you make? Do the same process with the cosine.
– Susan Socha

4.2.

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4.3.

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5.

Quadrilaterals

  • 1. Parallelogram 2
  • 2. Parallelogram Practice

5.1.

Parallelogram 2

– Ulli Skillman

5.2.

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6.

Area and Volume

  • 1. Cavalieri's Principle
  • 2. Principle of Parallel Slices in the Coordinate Plane
  • 3. Cavalieri's Principle
  • 4. Trisecting a Rectangular Prism (Improved)
  • 5. Square Cross Section: Finished Product
  • 6. right triangle paradox

6.1.

Cavalieri's Principle

Cavalieri's Principle applies in many contexts, but this is the most fundamental. This sketch was the idea of Jill Knaus (@JillKnaus) and goes with the start of a lesson plan for the Principle (Common Core HSG-GMD.A.2): [url]http://bit.ly/1hiHIUI[/url] The sketch asks: What do you notice? What can you change? Compare & contrast the triangles and their measures. What do you wonder about?

More GeoGebra at [url]mathhombre.blogspot.com[/url].
– John Golden

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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7.

Coordinate Geometry

  • 1. Module 4 Lesson 1
  • 2. Proportional Segments Using Ratios

7.1.

Module 4 Lesson 1

– Ulli Skillman

7.2.

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8.

Circles

  • 1. M5L2 1. Diameter and Chord
  • 2. M5L2 2.A. Congruent Chords
  • 3. M5L2 2.B. Equidistant Chords
  • 4. M5L2 3. Congruent Chords and Central Angles
  • 5. Inscribed Angle Demonstration
  • 6. Inscribed Quadrilateral
  • 7. M5 L11/12 Properties of Tangents (A)
  • 8. Properties of Tangents Drawn to Circles (B)
  • 9. Tangents, Secants and Central Angles
  • 10. Tangent-Secant angle at Radius
  • 11. M5 L14
  • 12. Angles and arcs of secant lines intersecting a circle
  • 13. Tangents to Circles: Investigation
  • 14. Tangent to Circle: Construction 1
  • 15. Lesson 9.2 Chord Properties 1
  • 16. ACCESS - Circles and Central Angles 1
  • 17. Parallel Lines and Intercepted Arcs
  • 18. Angles Outside Circle Theorems
  • 19. L17 Two Intersecting Chords in a Circle
  • 20. Two Intersecting Chords in a Circle
  • 21. Relationships of segment lengths from the intersection of secants, chords, and tangents of a circle
  • 22. Chords intersecting outside the circle
  • 23. ACCESS - Secants
  • 24. ACCESS - Secants and Tangents

8.1.

M5L2 1. Diameter and Chord

[color=#000000]Once you slide the slider in the applet below, you'll immediately notice a chord drawn and a[/color] [b][color=#6d9eeb]diameter drawn to this chord. [/color][/b][br][br][color=#000000]Interact with this applet for a few minutes, then answer the questions that follow. As always, be sure to change the locations of the BIG POINTS at any time before re-sliding the slider. [/color]
[color=#980000][b]Questions:[/b][/color][br][br][color=#000000]1) What does the movement of the[/color] [color=#ff00ff]pink angle[/color] [color=#000000]imply about [b]the intersection[/b] of the diameter and this chord? [/color][br][br][color=#000000]2) Fill in the blank: [br][br]In essence, the action you observed from the[/color] [color=#ff00ff]pink angle[/color] [color=#000000]implies that this[/color] [color=#3d85c6]diameter[/color] [color=#000000]and this chord are __________________. [/color][br][br][color=#000000]3) If a[/color] [color=#3d85c6]diameter[/color] [color=#000000]intersects a chord in the manner you've described in your response to (2) above, what does this[/color] [color=#3d85c6]diameter[/color] [color=#000000]do to this chord? How was this evidenced in the applet above? [br][/color][br][color=#000000]4) If a[/color] [color=#3d85c6]diameter[/color] [color=#000000]intersects a chord in the manner you've described in your response to (2) above, what does this[/color] [color=#3d85c6]diameter[/color] [color=#000000]do to[/color] [b][color=#000000]the entire arc[/color][/b] [color=#000000]this chord intercepts? How was this evidenced in the applet above? [br][br]5) Formally prove your responses to exercises (3) and (4) above using a 2-column format. [/color]
– Ulli Skillman, Tim Brzezinski

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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8.8.

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8.9.

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8.10.

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8.11.

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8.12.

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8.13.

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8.14.

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8.15.

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8.16.

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8.17.

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8.18.

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8.19.

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8.20.

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8.21.

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8.22.

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8.23.

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8.24.

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