Miss Reed's Book

Ashleigh, May 15, 2015

Miss Reed's book of GeoGebra lessons/worksheets.

Table of Contents

  1. Geometry
    1. Exploring Alternate Exterior Angles (V2)
    2. Exploring Corresponding Angles (V2)
    3. Alternate Interior Angles Theorem (V1)
    4. Same Side Interior Angles Theorem
    5. Perpendicular Bisector Definition
    6. A Special Theorem: Part 2 (V4)
    7. Incenter & Incircle Action!
    8. Incenter Exploration (A)
    9. Animation 28
    10. Triangle Proportionality and Angle Bisector
    11. Circle Equation: Center NOT (0,0)
    12. Equation of a Circle
    13. Regular Polygons: Perimeter & Area
    14. regular polygon area g6
    15. A tessellation with fishes (Escher).
    16. 1.4.2b Identifying Quadrilaterals
    17. 10-4 Inscribed Angles and Polygons-PART B
  2. Graphing
    1. 01 Learning Polar Graphing
    2. 02 Learning Polar Graphing
    3. 03 Learning Polar Graphing
  3. Algebra
    1. Pythagorean Theorem Worksheet
    2. The perfect Basketball shot

1.

Geometry

  • 1. Exploring Alternate Exterior Angles (V2)
  • 2. Exploring Corresponding Angles (V2)
  • 3. Alternate Interior Angles Theorem (V1)
  • 4. Same Side Interior Angles Theorem
  • 5. Perpendicular Bisector Definition
  • 6. A Special Theorem: Part 2 (V4)
  • 7. Incenter & Incircle Action!
  • 8. Incenter Exploration (A)
  • 9. Animation 28
  • 10. Triangle Proportionality and Angle Bisector
  • 11. Circle Equation: Center NOT (0,0)
  • 12. Equation of a Circle
  • 13. Regular Polygons: Perimeter & Area
  • 14. regular polygon area g6
  • 15. A tessellation with fishes (Escher).
  • 16. 1.4.2b Identifying Quadrilaterals
  • 17. 10-4 Inscribed Angles and Polygons-PART B

1.1.

Exploring Alternate Exterior Angles (V2)

In the applet below, a [b]TRANSVERSAL[/b] intersects [b]2 PARALLEL LINES[/b]. [br][br]When this happens, there are 2 pairs of [b][color=#b20ea8]ALTERNATE EXTERIOR ANGLES[/color][/b] that are formed. [br][br]Interact with the applet below for a few minutes, then answer the questions that immediately follow.
[color=#c51414][b]Directions & Questions:[/b] [/color][br][br]1) Complete the following statement: I[b]f a transversal intersects 2 ________________  ______________, then [color=#b20ea8]alternate exterior angles[/color] are _____________________.[/b] [br][br]2) If the pink angle above measures 146 degrees, what would the measure of its alternate exterior angle be?  What would the measure of the gray angle be?  [br][br]3) As you moved the slider, what transformation(s) took place? 
– Tim Brzezinski

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1.5.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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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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2.

Graphing

  • 1. 01 Learning Polar Graphing
  • 2. 02 Learning Polar Graphing
  • 3. 03 Learning Polar Graphing

2.1.

01 Learning Polar Graphing

A polar grid consists of a sequence of concentric circles that are divided radially by various radial lines at regular angular divisions usually in increments of 5°, 10°, or 15°. Periodically you may want [color=#1551b5][b]Press the Recycle Icon[/b][/color] on the upper right to clear the worksheet. GeoGebra contains three commands that will assist us in creating the polar grid. Circle[Point M, Number r], Line[Point, Direction vector v], and Sequence[Expression, Variable i, Number a, Number b, <Increment>] To draw a circle with a center at Point(4,5) and radius = 3, we would enter the following command in the input line: Circle[(4, 5), 3] {You should try this entry and others prior to proceeding.} To draw a line that starts at the point (4, 5) toward the end of the direction vector of 4x + 5y = 12 or (5, -4), we type the following Line[(4, 5),(5, -4)] in the input line. "A line with equation ax + by = c has the Direction vector (b, -a)." {You should try this entry and others prior to proceeding.} To draw a line through the origin at a 15° angle type: Line[(0, 0), (cos(15°), sin(15°))] The final important command is Sequence. This command allows incremental copies of an expression to be graphed. To create a simple family of parabolas type: Sequence[a x2, a, -2, 2]. The sequence automatically increments by ones, this can be change by typing: Sequence[a x2, a, -2, 2, 0.5] The following command will create 40 concentric circle centered at the origin by 1/2 unit increments: polarCircles = Sequence[Circle[(0, 0), k / 2], k, 1, 20] The following command will create a series of radial lines at increments from 0 through 175° in 15° increments: radialLines = Sequence[Line[(0, 0), (cos(a), sin(a))], a, 0, 175°, 15°] The Parametric Curve Command allows us to create or graph polar functions. Curve[Expression e1, Expression e2, Parameter t, Number a, Number b]: Yields the Cartesian parametric curve for the given x-expression e1 and y-expression e2 (using parameter t) within the given interval [a, b]. r(x) = 1 {hide this line, this function will allow you to enter polar equations} Curve[r(i) cos(i), r(i) sin(i), i, 0, 2 pi] {this will draw a circle of radius one}

This instructional construction is for students and teachers to learn how to use parametric curve command to graph polar graphs.
– Auston B Cron

2.2.

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3.

Algebra

  • 1. Pythagorean Theorem Worksheet
  • 2. The perfect Basketball shot

3.1.

Pythagorean Theorem Worksheet

Proving Pythagorean Theorem
– Linda, kethom5

3.2.

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