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Beginner Tutorials
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1. Beginner Exercises (1)
- Creating Regular Polygons: Ex. 1
- Using Circle and Intersect Tools: Ex. 2
- Using the Compass Tool: Ex. 3
- Measuring Angles: Ex. 4
- Isosceles Triangle Exp: Ex. 5A
- Isosceles Triangle Exp: Ex. 5B
- Constructing Angles: Ex. 6
- Parallels & Perpendiculars: Ex. 7
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2. Beginner Exercises (2)
- Working With Midpoints: Ex. 8
- Making Perpendicular Bisectors: Ex. 9
- Vertical Angles Discovery: Ex. 10
- Constructing Angle Bisectors: Ex. 11
- Constructing Tangents: Ex. 12
- Sliders & Circles Discovery: Ex. 13
- Controlling Angles with Sliders: Ex. 14
- Exploring Slopes of Lines: Ex. 15
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3. Beginner Exercises (3)
- Translating by Vector: Ex. 16
- Rotating Around Points: Ex. 17
- Reflecting About Lines: Ex. 18
- Exploring Dilations: Ex. 19
- Composing Transformations: Ex. 20
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Beginner Tutorials
Tim Brzezinski, Emily Davis, Nov 27, 2018
Table of Contents
- Beginner Exercises (1)
- Creating Regular Polygons: Ex. 1
- Using Circle and Intersect Tools: Ex. 2
- Using the Compass Tool: Ex. 3
- Measuring Angles: Ex. 4
- Isosceles Triangle Exp: Ex. 5A
- Isosceles Triangle Exp: Ex. 5B
- Constructing Angles: Ex. 6
- Parallels & Perpendiculars: Ex. 7
- Beginner Exercises (2)
- Working With Midpoints: Ex. 8
- Making Perpendicular Bisectors: Ex. 9
- Vertical Angles Discovery: Ex. 10
- Constructing Angle Bisectors: Ex. 11
- Constructing Tangents: Ex. 12
- Sliders & Circles Discovery: Ex. 13
- Controlling Angles with Sliders: Ex. 14
- Exploring Slopes of Lines: Ex. 15
- Beginner Exercises (3)
- Translating by Vector: Ex. 16
- Rotating Around Points: Ex. 17
- Reflecting About Lines: Ex. 18
- Exploring Dilations: Ex. 19
- Composing Transformations: Ex. 20
Creating Regular Polygons: Ex. 1
DIRECTIONS:
In the GeoGebra applet below,
1) Select the REGULAR POLYGON 
tool. Then plot 2 points A and B.
In the pop-up box that appears, enter "3" (without the " ").
This creates an "regular triangle" (equilateral & equiangular triangle).
2) Now use this same tool to construct a regular quadrilateral (square) and regular octagon.
3) Select the MOVE 
tool. Move any one (or more) of the blue points around.
Note these polygons always remain regular.
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.
tool. Then plot 2 points A and B.
In the pop-up box that appears, enter "3" (without the " ").
This creates an "regular triangle" (equilateral & equiangular triangle).
2) Now use this same tool to construct a regular quadrilateral (square) and regular octagon.
3) Select the MOVE tool. Move any one (or more) of the blue points around.
Note these polygons always remain regular.
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.
Quick (Silent) Demo
Beginner Exercises (2)
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1. Working With Midpoints: Ex. 8
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2. Making Perpendicular Bisectors: Ex. 9
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3. Vertical Angles Discovery: Ex. 10
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4. Constructing Angle Bisectors: Ex. 11
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5. Constructing Tangents: Ex. 12
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6. Sliders & Circles Discovery: Ex. 13
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7. Controlling Angles with Sliders: Ex. 14
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8. Exploring Slopes of Lines: Ex. 15
Working With Midpoints: Ex. 8
DIRECTIONS:
1) Use the MIDPOINT 
tool to plot the midpoints of any 2 sides of the given triangle.
2) Use the SEGMENT 
tool to draw the segment (triangle midsegment) connecting these 2 points.
3) Use ANOTHER TOOL to illustrate this midsegment (MS) is parallel to the 3rd side of the triangle.
4) Measure and display the names lengths of the MS and the side of the triangle the MS doesn't touch.
5) In the algebra view (left side), input [name of MS] / [name of triangle side MS doesn't touch].
6) Move A, B, and/or C around to verify the slopes are equal and the ratio MS / 3rd side = 0.5.
tool to plot the midpoints of any 2 sides of the given triangle.
2) Use the SEGMENT tool to draw the segment (triangle midsegment) connecting these 2 points.
3) Use ANOTHER TOOL to illustrate this midsegment (MS) is parallel to the 3rd side of the triangle.
4) Measure and display the names lengths of the MS and the side of the triangle the MS doesn't touch.
5) In the algebra view (left side), input [name of MS] / [name of triangle side MS doesn't touch].
6) Move A, B, and/or C around to verify the slopes are equal and the ratio MS / 3rd side = 0.5. 7)
Can you use YET ANOTHER TOOL to prove the midsegment is parallel to the 3rd side of the triangle?
Do so.
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Yes: Measure a pair of corresponding angles (as done at 1:59 in the screencast) and show that they always remain congruent!
If a transversal intersects two lines (or segments) so that it forms a pair of congruent corresponding angles, then those lines (or segments) are parallel.
Teachers:
Here is one easy, yet powerfully effective means for students to actively discover the Triangle Midsegment Theorem for themselves.
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.
Quick (Silent) Demo
Translating by Vector: Ex. 16
DIRECTIONS:
In the applet below,
1) Construct a triangle.
2) Use the VECTOR TOOL 
to construct any vector whose terminal points DOES NOT lie on top of its initial point.
3) Display the label of the triangle's 3 vertices and vector you've just constructed.
Use the "Name and Value" option when showing the label.
4) Use the TRANSLATE BY VECTOR TOOL 
to translate the triangle by the given vector.
to construct any vector whose terminal points DOES NOT lie on top of its initial point.
3) Display the label of the triangle's 3 vertices and vector you've just constructed.
Use the "Name and Value" option when showing the label.
4) Use the TRANSLATE BY VECTOR TOOL to translate the triangle by the given vector. 5)
Suppose the coordinates of a point P = (x, y). What is the image of P under a translation by vector with components <a, b>?
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Coordinates of Image = (x + a, y + b)
When you're done (or if you're unsure of something), feel free to check by watching the quick silent screencast below the applet.
Quick (Silent) Demo
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