Cleveland Geometry

Hannah Ingham, Oct 24, 2015

Lab Investigation--Properties of Circles

Table of Contents

  1. Triangle Properties
    1. The Ambiguous Case
    2. Ambiguous Case of Side-Side-Angle Triangle
    3. Side-Side-Side Congruency
    4. ASA congruence
    5. Alternate interior angles
    6. Alternate Exterior Angles
    7. Translation
    8. Converse of Pythagorean Theorem
    9. SAS Similarity Investigation
    10. AA Triangle Similarity Investigation
    11. SSS Similarity Investigation
  2. Polygonal Properties
    1. Regular Polygon
    2. Polygons & Angles
    3. Will It Tessellate?
    4. Polygon Definitions
    5. Sum of exterior angles of a polygon
    6. Determining the properties of a Parallelogram
    7. Properties: parallelogram
    8. Tranlation-4
    9. Rotations Exploration
    10. Area of a Regular Polygon
    11. Net of a Dodecahedron
    12. Classic net of the cube
    13. Nets of Tetrahedron
    14. Net of Hexagonal Prism
    15. Net of a Square Pyramid
    16. Net of a Cylinder
    17. Net of a Cone
    18. Net of Pyramid
    19. Net of a triangular prism
  3. Circle Properties
    1. Congruent Chords and their Central Angles - Large Font
    2. Congruent Chords and Distance from Center
    3. Circle arc radian
    4. A Rolling Circle
    5. Tangent Lines and Inscribed Angles
    6. Construction of Tangents to a circle
    7. Inscribed Angle Properties
    8. Inscribed Angle Theorem
    9. Arc Length Pizza Crust Model
    10. Discovering the Equation of the Circle
  4. Circle Sectors, Area, & Circumference
    1. Example 1
    2. Area of a Circle - Wedge Demo 1
    3. Area of a Circle - Wedge/Sector Demonstration
    4. Archimedes' Simulation of Pi Calculation upto 200-gon
    5. Inscribed and Circumscribed Polygons
  5. 6.2 Tangent Properties
    1. Review Circle Terms
    2. Tangent Line
    3. Define Secant Line
    4. Comparing Tangent and Secant Lines
    5. Tangent Segments Conjecture
    6. Construct a Tangent Line From a Point Outside a Circle
  6. 6.3 Arcs and Angles
    1. Circle Vocabulary Exploration
    2. Central and Inscribed Angles
    3. Inscribed Angles and Central Angle
    4. Relationship between central and inscribed angles
    5. Angles Inscribed in a Semicircle
    6. Cyclic Quadrilaterals Exploration
    7. Parallel Lines and Intercepted Arcs
  7. Challenge Proofs
    1. the famous "1/5" square
    2. supplementary angles
    3. square vs rhombus
  8. Refresh
    1. Number Line Integer Sum Exploration
    2. Compare Fractions
  9. Geometry of Solids
    1. Principi de Cavalieri per prismes oblics
    2. All solids of Platon rotate
    3. Volume of Sphere Proof
    4. Faces, Vertices and Edges of a Cube
    5. Volume of a Rectangular Prism
    6. Cube Trisection
  10. Trigonometry
    1. Right Triangle Exploration
    2. Investigating Trigonometry 3
    3. Investigating Trigonometry Functions
    4. right triangle trigonometry-1
    5. Find Building Height
    6. Geometry problem
    7. the height of the pyramid

1.

Triangle Properties

  • 1. The Ambiguous Case
  • 2. Ambiguous Case of Side-Side-Angle Triangle
  • 3. Side-Side-Side Congruency
  • 4. ASA congruence
  • 5. Alternate interior angles
  • 6. Alternate Exterior Angles
  • 7. Translation
  • 8. Converse of Pythagorean Theorem
  • 9. SAS Similarity Investigation
  • 10. AA Triangle Similarity Investigation
  • 11. SSS Similarity Investigation

1.1.

The Ambiguous Case

An illustration of the ambiguous case for ASS.
– Kevin Krenz

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1.7.

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1.10.

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1.11.

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2.

Polygonal Properties

  • 1. Regular Polygon
  • 2. Polygons & Angles
  • 3. Will It Tessellate?
  • 4. Polygon Definitions
  • 5. Sum of exterior angles of a polygon
  • 6. Determining the properties of a Parallelogram
  • 7. Properties: parallelogram
  • 8. Tranlation-4
  • 9. Rotations Exploration
  • 10. Area of a Regular Polygon
  • 11. Net of a Dodecahedron
  • 12. Classic net of the cube
  • 13. Nets of Tetrahedron
  • 14. Net of Hexagonal Prism
  • 15. Net of a Square Pyramid
  • 16. Net of a Cylinder
  • 17. Net of a Cone
  • 18. Net of Pyramid
  • 19. Net of a triangular prism

2.1.

Regular Polygon

Dynamically set vertices for a regular polygon
Regular Polygon
– tyler.wendell

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2.6.

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2.11.

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2.13.

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2.15.

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2.16.

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2.17.

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2.18.

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2.19.

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3.

Circle Properties

  • 1. Congruent Chords and their Central Angles - Large Font
  • 2. Congruent Chords and Distance from Center
  • 3. Circle arc radian
  • 4. A Rolling Circle
  • 5. Tangent Lines and Inscribed Angles
  • 6. Construction of Tangents to a circle
  • 7. Inscribed Angle Properties
  • 8. Inscribed Angle Theorem
  • 9. Arc Length Pizza Crust Model
  • 10. Discovering the Equation of the Circle

3.1.

Congruent Chords and their Central Angles - Large Font

Use this applelt to explore the properties of central angles and arcs formed by congruent chords in a circle.
Congruent Chords and their Central Angles - Large Font
– blisardd

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3.8.

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3.10.

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4.

Circle Sectors, Area, & Circumference

  • 1. Example 1
  • 2. Area of a Circle - Wedge Demo 1
  • 3. Area of a Circle - Wedge/Sector Demonstration
  • 4. Archimedes' Simulation of Pi Calculation upto 200-gon
  • 5. Inscribed and Circumscribed Polygons

4.1.

Example 1

A circle has a radius of [math]24[/math] units. Find the area of a sector with a central angle of [math]30^\circ[/math].
[list=1][br][*]Find the area of the circle.[br][*]Set up a proportion.[br][*]Multiply both sides by the area of the circle to find the area of the sector.[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.
– Walch Education

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5.

6.2 Tangent Properties

  • 1. Review Circle Terms
  • 2. Tangent Line
  • 3. Define Secant Line
  • 4. Comparing Tangent and Secant Lines
  • 5. Tangent Segments Conjecture
  • 6. Construct a Tangent Line From a Point Outside a Circle

5.1.

Review Circle Terms

Drag points on the circle below to change the figure. Look for examples of circle terms such as radii, chords, inscribed angles, central angles, and arcs.
– Hannah Ingham

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6.

6.3 Arcs and Angles

  • 1. Circle Vocabulary Exploration
  • 2. Central and Inscribed Angles
  • 3. Inscribed Angles and Central Angle
  • 4. Relationship between central and inscribed angles
  • 5. Angles Inscribed in a Semicircle
  • 6. Cyclic Quadrilaterals Exploration
  • 7. Parallel Lines and Intercepted Arcs

6.1.

Circle Vocabulary Exploration

A dynamic illustration of some of the terms we use to talk about circles. [br][br]Click the terms to see these terms highlighted on the figures. [br][br]Follow instructions for Task 1 and Task 2 on the figure
Circle Vocabulary Exploration
– Hannah Ingham, John Golden

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7.

Challenge Proofs

  • 1. the famous "1/5" square
  • 2. supplementary angles
  • 3. square vs rhombus

7.1.

the famous "1/5" square

– sonom

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8.

Refresh

  • 1. Number Line Integer Sum Exploration
  • 2. Compare Fractions

8.1.

Number Line Integer Sum Exploration
– Hannah Ingham

8.2.

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9.

Geometry of Solids

  • 1. Principi de Cavalieri per prismes oblics
  • 2. All solids of Platon rotate
  • 3. Volume of Sphere Proof
  • 4. Faces, Vertices and Edges of a Cube
  • 5. Volume of a Rectangular Prism
  • 6. Cube Trisection

9.1.

Principi de Cavalieri per prismes oblics
– Juli Jurado i Llamas

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10.

Trigonometry

  • 1. Right Triangle Exploration
  • 2. Investigating Trigonometry 3
  • 3. Investigating Trigonometry Functions
  • 4. right triangle trigonometry-1
  • 5. Find Building Height
  • 6. Geometry problem
  • 7. the height of the pyramid

10.1.

Right Triangle Exploration
– vinylmath, youngcar, Hannah Ingham

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