My Geometry GeoGebra Book

mark vasicek, Dec 8, 2017

Table of Contents

  1. Conjectures
    1. Making Conjectures (1)
    2. Making Conjectures (2)
    3. Making Conjectures (3)
    4. Making Conjectures (4)
    5. Making Conjectures (5)
  2. Parallel / Perpendicular
    1. Parallel & Perpendicular Consequence
    2. Triangle Angle Sum Theorem
  3. Triangles
    1. ASA
    2. Exterior Angle Theorem
    3. Copy of Copy of Exterior Angle Theorem
    4. Copy of Angle Sum of Triangle
    5. Interior and Exterior Angles of a Heptagon.
    6. Exterior Angles of a Heptagon
  4. Triangle Centers
    1. Centroid (G) - Center of Gravity - Concurrent at medians.
    2. Circumcenter (C) - concurrent at perpendicular bisectors - circumcenter, circumradius, circumcircle
    3. Orthocenter (H) - concurrent at altitudes
    4. Incenter (I) - concurrent at angle bisectors - incenter incircle inradius
    5. Explore Triangle Centers
    6. pavillion
    7. Pizza Problem
  5. Quadrilaterals
    1. Quad-A
    2. Quad-B
    3. Quad-C
    4. Quad-D
    5. Quad-E
    6. Quad-F
    7. Quad-G
    8. Quad-H

1.

Conjectures

  • 1. Making Conjectures (1)
  • 2. Making Conjectures (2)
  • 3. Making Conjectures (3)
  • 4. Making Conjectures (4)
  • 5. Making Conjectures (5)

1.1.

Making Conjectures (1)

Conjectures
[br]The drawing has specific information marked. You are given the ability to do a drag test by selecting points that are marked and moving them about.[br][br]Use the information shown and what you can gather from doing the drag test to make as many conjectures as you can. Can you come up with a way to test those conjectures?
– mark vasicek

1.2.

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1.3.

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1.4.

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1.5.

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2.

Parallel / Perpendicular

  • 1. Parallel & Perpendicular Consequence
  • 2. Triangle Angle Sum Theorem

2.1.

Parallel & Perpendicular Consequence

[color=#000000]The following applet demonstrates a property that parallel lines have when they're drawn in the coordinate plane. [br] [i] [br]Be sure to move the [color=#1e84cc][b]blue points[/b][/color] around quite a bit![/i] [/color]
[color=#000000]This applet demonstrates a property that perpendicular lines have when they're drawn in the coordinate plane. [br][br][i]Be sure to move the points around quite a bit and observe carefully as you do! [/i][/color]
[color=#000000]What can you conclude about parallel lines drawn in the coordinate plane? [/color]
[color=#000000]What can you conclude about perpendicular lines that are drawn in the coordinate plane? [br](Assume the lines are not aligned horizontally and vertically). [/color]
– mark vasicek, Tim Brzezinski

2.2.

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3.

Triangles

  • 1. ASA
  • 2. Exterior Angle Theorem
  • 3. Copy of Copy of Exterior Angle Theorem
  • 4. Copy of Angle Sum of Triangle
  • 5. Interior and Exterior Angles of a Heptagon.
  • 6. Exterior Angles of a Heptagon

3.1.

ASA

– forresterk

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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4.

Triangle Centers

  • 1. Centroid (G) - Center of Gravity - Concurrent at medians.
  • 2. Circumcenter (C) - concurrent at perpendicular bisectors - circumcenter, circumradius, circumcircle
  • 3. Orthocenter (H) - concurrent at altitudes
  • 4. Incenter (I) - concurrent at angle bisectors - incenter incircle inradius
  • 5. Explore Triangle Centers
  • 6. pavillion
  • 7. Pizza Problem

4.1.

Centroid (G) - Center of Gravity - Concurrent at medians.

Centroid (G) - Center of gravity) - concurrent at medians
– mark vasicek

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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5.

Quadrilaterals

  • 1. Quad-A
  • 2. Quad-B
  • 3. Quad-C
  • 4. Quad-D
  • 5. Quad-E
  • 6. Quad-F
  • 7. Quad-G
  • 8. Quad-H

5.1.

Quad-A

Do the drag test on each of the vertices. [br]Use your knowledge of polygons to try to figure out what kind of polygon this is.[br][br]Tell all you can about the figure. You may want to consider looking at sides angles and diagonals.[br][br]Is one pair of opposite sides parallel? Are both?[br]Are any sides congruent? Are the congruent sides opposite each other? Are they adjacent?[br][br]Are angles congruent? Is one pair of opposite angles congruent? Are both pair of opposite angles congruent? [br][br]Do diagonals bisect each other? Are diagonals congruent? Are diagonals perpendicular?
– mark vasicek

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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