Geometry

Auston B Cron, Ronan Downes, Mar 15, 2020

This book will cover topics in Geometry [color=#c51414][b]G[/b]eneral [b]E[/b]ducational [b]D[/b]evelopment[/color] (GED) tests are a group of four subject tests which, when passed, certify that the test taker has American or Canadian high school-level academic skills. Here are some topics which can assist students in learning the mathematics covered on the GED/HiSET/TASC/GCSE [color=#c51414][b]G[/b]eneral [b]C[/b]ertificate of [b]S[/b]econdary [b]E[/b]ducation[/color]. Book 1 is a compilation of basic skills needed for success, but not tested. [b]Mostly PreGED Skills[/b] Book 2 has many activities which are tested. [b]Many GED Level Skills[/b] [b]GED Mathematics Book1[/b] [url]https://www.geogebra.org/m/j4UyPdKW[/url] [b]GED Mathematics Book 2[/b] [url]https://www.geogebra.org/m/mEs37yMj[/url] [b]GED Science[/b] [url]https://www.geogebra.org/m/kH5xMUpw[/url] [b]GED Slope[/b] [url]https://www.geogebra.org/m/cvAySD7E[/url] Thanks, Tim B. [b]Geometry Introduction[/b] [url]https://www.geogebra.org/m/dsGHMH8u[/url]

Table of Contents

  1. Basic Terminology
    1. Basic Terms in Geometry
    2. Triangle Inequality
    3. Finding sums of angles
    4. What class of Triangles use Pythagorean Theorem?
    5. Triangle: Sum of Interior Angles
    6. Parallel Lines & Related Angles
    7. Intersecting Line Properties
    8. Classify Triangles by Angle
    9. Supplementary Angles (Quick Exploration)
    10. Complementary Meaning?
    11. PolygonTypes
    12. Regular Polygons (with Limits)
  2. Circles and Arcs
    1. Minor and Major Arcs of a Circle
  3. Circle Relationships
    1. Circle Relationships (IN or ON)
    2. Circle Relationships (Out)
    3. Circle Relationships (segments)
    4. Full Circle Protractors
  4. Constructions
    1. Construct a cirle given 3 points
    2. Construct a Central Angle
    3. Inscribed Angle
    4. Parallel & Perpendicular Linear Equations
    5. Triangle Inequality
    6. Triangle: Sum of Remote Interior Angles & Exterior Angle
    7. Triangle: Proportionality
    8. Parallel Line Theorems
    9. Quadrilateral Tools
    10. Triangle Centers
  5. Pythagoras
    1. Pythagorean Triple Generator
    2. Polygon Proofs of Pythagoras
    3. Spiral of Pythagoras
    4. All Poly Proof of Pythagoras
    5. Pythagorean Proof SemiCircle
    6. Deriving the Quadratic Formula using Completing the Square (v.2)
    7. Area of Regular Polygon
  6. Conics
    1. General Equation of Parabola (origin)
    2. General Equation of Parabola (transform)
    3. General Equation of Circle (origin)
    4. General Equation of Circle (origin)
    5. General Equation of Ellipse (origin)
    6. General Equation of Ellipse (translated)
    7. General Equation of Hyperbola (origin)
    8. General Equation of Hyperbola (transform)
    9. Volume of Sphere Proof
  7. Triangle Properties
    1. Classify Triangles by Angle
    2. Classify Triangles by Sides and Angles
    3. Pythagorean Theorem (Converse)
  8. Quadrilaterals
    1. LinkedIn Trapezoids
    2. Varignon Parallelogram
    3. Convex quadrilaterals
  9. Angles
    1. Angle Info
    2. Defining the Coterminal Angle
    3. Finding sums of angles
    4. Standard Position (Improved)
    5. Intersecting Line Properties
    6. Degrees vs Radians
    7. Convert Radians with Degrees

1.

Basic Terminology

  • 1. Basic Terms in Geometry
  • 2. Triangle Inequality
  • 3. Finding sums of angles
  • 4. What class of Triangles use Pythagorean Theorem?
  • 5. Triangle: Sum of Interior Angles
  • 6. Parallel Lines & Related Angles
  • 7. Intersecting Line Properties
  • 8. Classify Triangles by Angle
  • 9. Supplementary Angles (Quick Exploration)
  • 10. Complementary Meaning?
  • 11. PolygonTypes
  • 12. Regular Polygons (with Limits)

1.1.

Basic Terms in Geometry

This lessons reviews Basic Geometry Vocabulary with interactive displays of the vocabulary.[br][br]Point(s), Plane, Line, Segment, Ray, Angle, Side(s), Vertex, etc.
Additional resources to view:[br]Standard Position 01[br]Standard Position 01a[br]Coterminal Angles 01b
– Auston B Cron

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1.8.

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1.10.

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1.11.

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1.12.

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2.

Circles and Arcs

  • 1. Minor and Major Arcs of a Circle

2.1.

Minor and Major Arcs of a Circle

This is an examination of the minor and major arcs of a circle.[br]The definition of an arc, a minor arc, and a major are listed.
There is a note describing how Arc[<conic>,<point>, <point>] works...
– Auston B Cron

3.

Circle Relationships

  • 1. Circle Relationships (IN or ON)
  • 2. Circle Relationships (Out)
  • 3. Circle Relationships (segments)
  • 4. Full Circle Protractors

3.1.

Circle Relationships (IN or ON)

Level 1: 2 secant lines (intersecting at an internal point) Level 2: 2 secant lines (intersecting at on the circle) Level 3: 1 Tangent & 1 secant (intersecting at on the circle)

Activate only 1 check box at a time...
– Auston B Cron

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4.

Constructions

  • 1. Construct a cirle given 3 points
  • 2. Construct a Central Angle
  • 3. Inscribed Angle
  • 4. Parallel & Perpendicular Linear Equations
  • 5. Triangle Inequality
  • 6. Triangle: Sum of Remote Interior Angles & Exterior Angle
  • 7. Triangle: Proportionality
  • 8. Parallel Line Theorems
  • 9. Quadrilateral Tools
  • 10. Triangle Centers

4.1.

Construct a cirle given 3 points

Use the tools indicated to plot 3 points, connect two segments connecting the point, construct perpendicular bisectors of each segment; the intersection of the bisectors is the center of the circle; finally draw the circle and report the size of the radius.

ToolImage[0] Move image ToolImage[1] Point ToolImage[15] Segment ToolImage[8] Perpendicular Bisector ToolImage[10 ] Circle ToolImage[40] Move Graphics View ToolImage[41] Zoom Out ToolImage[42] Zoom In
– Auston B Cron

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5.

Pythagoras

  • 1. Pythagorean Triple Generator
  • 2. Polygon Proofs of Pythagoras
  • 3. Spiral of Pythagoras
  • 4. All Poly Proof of Pythagoras
  • 5. Pythagorean Proof SemiCircle
  • 6. Deriving the Quadratic Formula using Completing the Square (v.2)
  • 7. Area of Regular Polygon

5.1.

Pythagorean Triple Generator

This applet displays Pythagorean Triple integer values when they exist.
a = m² + n² [br]b = 2mn [br]c = m² - n² [br]m > n
– Auston B Cron

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6.

Conics

  • 1. General Equation of Parabola (origin)
  • 2. General Equation of Parabola (transform)
  • 3. General Equation of Circle (origin)
  • 4. General Equation of Circle (origin)
  • 5. General Equation of Ellipse (origin)
  • 6. General Equation of Ellipse (translated)
  • 7. General Equation of Hyperbola (origin)
  • 8. General Equation of Hyperbola (transform)
  • 9. Volume of Sphere Proof

6.1.

General Equation of Parabola (origin)

Three sliders, a, b, and α adjust the general equation of a parabola. a and b set the major and minor axis and α allows the parabola to rotate. Display of [math]\frac {(x-h)²}{a²} + \frac{(y-k)}{b} = 1[/math]

What are the setting ranges for a, b, and α to show a vertical parabola? A horizontal parabola? What settings changes are needed to set the rotation of the parabola to 45°, 120°, 215°, or 330°? A parabola has a vertex, a focus, and a directrix, what setting does the b represent with respect to these values? What about the a value?
– Auston B Cron

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7.

Triangle Properties

  • 1. Classify Triangles by Angle
  • 2. Classify Triangles by Sides and Angles
  • 3. Pythagorean Theorem (Converse)

7.1.

– Auston B Cron

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8.

Quadrilaterals

  • 1. LinkedIn Trapezoids
  • 2. Varignon Parallelogram
  • 3. Convex quadrilaterals

8.1.

LinkedIn Trapezoids

Quick demo for trapezoid.. Can show other quadrilaterals as well.

[url]https://www.linkedin.com/groupAnswers?viewQuestionAndAnswers=&discussionID=5872687280061169666&gid=33207&commentID=5875084224502992896&trk=view_disc&fromEmail=&ut=13ESSbMwZjemg1[/url]
– Auston B Cron

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9.

Angles

Information about angles.

  • 1. Angle Info
  • 2. Defining the Coterminal Angle
  • 3. Finding sums of angles
  • 4. Standard Position (Improved)
  • 5. Intersecting Line Properties
  • 6. Degrees vs Radians
  • 7. Convert Radians with Degrees

9.1.

Angle Info

Any of the points are moveable.[br][br]Showing methods to name angles with points.[br]Showing name of type of angle:[br] Acute, Right, Obtuse, and Reflex
Angles can be assigned numerical names as well. This is done when there are a lot of angles to be named.
– Auston B Cron

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Information