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Symmetry
to y-axis
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Construction
1. Create
any triangle.
2. Display the axes.
3. Create the triangle reflection through the y-axis.
Investigation
A. Explore the reflection
properties.
B. Summarize the corresponding points of the two triangles and their
distance from the vertical axis.
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Translation
With Coordinate System |
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Construction
1. Create
any triangle.
2. Display the axes.
3. Move the triangle 18 units to the right and 5 units up.
Investigation
A. Explore the translation
properties.
B. What is the connection between the coordinates of the original
triangle and the translated one?
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Reflection Through
a Given Line |
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Construction
1. Create
any triangle.
2. Draw a line.
3. Create a reflection of the triangle through the line.
Investigation
A. Explore the reflection's
properties. What connections can you find between the two triangles
and the line?
B. What examples of reflections do you come across in daily life?
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Rotation
About a Point
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Construction
1. Create
a triangle ABC.
2. Rotate the triangle about vertex B, and create the rotated
triangles.
Investigation
A. What is the effect of the
rotation? Are any of the triangle's properties changed?
B. Rotate the triangle again but this time rotate about a point
outside the triangle. Repeat the previous investigation.
C. Repeat the experiment with any polygon and summarize the results.
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Create a Circle
Greater/Smaller by a Desired Factor |
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Construction
1. Draw
a circle with center A whose circumference is twice as long.
2. Draw another concentric circle whose area is twice as large.
Investigation
A. Draw the radii of these
circles and find their ratio.
B. Explain the result.
C. Repeat the procedure using different ratios and explore :
(a) The ratio of the radii
(b) The ratio of the circumferences.
(c) The ratio of the areas.
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Create a Polygon
Greater/Smaller by a Desired Factor |
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Construction
1. Draw
a polygon.
2. Draw a polygon whose sides are 1.5 longer than the first polygon.
Investigation
A. What is the ratio of the two
perimeters?
B. What is the ratio of the two areas?
C. If a polygon's perimeter is four times as long as another
polygon's perimeter, what will be the ratio of the two polygons'
areas ?
D. If a polygon's area is four times as large as the area of another
polygon, what will be the ratio of the two polygons' perimeters?
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