Reflections on the Geometer’s
Sketchpad
Name
1. Draw triangle CDE and line AB so that the line does not intersect the figure. Reflect triangle CDE over line AB and gather the following information.
a)
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DE |
D’E’ |
CD |
C’D’ |
CE |
C’E’ |
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mÐDCE |
mÐD’C’E’ |
mÐCDE |
mÐC’D’E’ |
mÐCED |
mÐC’E’D’ |
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b) Which segments have the same lengths?
c) Which angles have the same measure?
d) Draw the segment connecting C to the midpoint of DE. Reflect this segment over line AB. Make two conclusions concerning the image.
e) Draw CC’. Label its intersection with line AB as point X. Measure angle CXB and C’XA and write those measurements on the line below. What conclusion can you make about the relationship between line AB and segment CC’?
f) Draw segment DE’ and segment ED’. Label their intersection Y. What is the location of Y? What conclusions can you make?
2. Repeat the previous data gathering and drawings for a triangle CDE where line AB intersects the figure at one point.
a)
|
DE |
D’E’ |
CD |
C’D’ |
CE |
C’E’ |
|
|
|
|
|
|
|
|
mÐDCE |
mÐD’C’E’ |
mÐCDE |
mÐC’D’E |
mÐCED |
mÐC’E’D’ |
|
|
|
|
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|
b)
c)
d)
e)
f)
3. Repeat the previous data gathering and drawings for a triangle CDE where line AB intersects the figure at two points.
a)
|
DE |
D’E’ |
CD |
C’D’ |
CE |
C’E’ |
|
|
|
|
|
|
|
|
mÐDCE |
mÐD’C’E’ |
mÐCDE |
mÐC’D’E |
mÐCED |
mÐC’E’D’ |
|
|
|
|
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|
b)
c)
d)
e)
f)
