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Symmetry
Similarity
Part 1 (Conditions of Similar Triangles)
Part 2 (Problem Solving)
Areas and Volumes
Part 1 (for Similar Figures)
Part 2 (for nonSimilar Figures)
Areas and Volumes
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Areas and Volumes (for Similar and nonsimilar figures)
(1) AREAs for Similar Figures
If figures are similar, the
ratios
of the lengths, widths and even perimeters are the same.
[Note:
ratio
can be seen as "
scale factor
".]
[Picture]
http://www.nctm.org/standards/content.aspx?id=26770
Click Me
(a) Use the applet to
show
that the ratios of the lengths, widths and even perimeters are the same
(b) Is the
ratio of the LENGTHs
the same as
ratio of the AREAs
?
i) Are the 2 ratios related?
ii) Do we need to find the
actual areas
(of both the figures) in order to find the ratio?
(2) AREAs and VOLUMEs for Similar Figures
Now that we know that (l1/l2)^2 = A1/A2
Is there any relationship between the (a)ratio of the lengths and (b)ratio of the Areas with ratio of the Volumes?
[Picture]
http://www.nctm.org/standards/content.aspx?id=25097
Click Me
Areas and Volumes
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Areas and Volumes (for Similar and nonsimilar figures)
(1) AREAs for Similar Figures
If figures are similar, the ratios of the lengths, widths and even perimeters are the same.[Note: ratio can be seen as "scale factor".]
http://www.nctm.org/standards/content.aspx?id=26770
(a) Use the applet to show that the ratios of the lengths, widths and even perimeters are the same
(b) Is the ratio of the LENGTHs the same as ratio of the AREAs?
i) Are the 2 ratios related?
ii) Do we need to find the actual areas (of both the figures) in order to find the ratio?
(2) AREAs and VOLUMEs for Similar Figures
Now that we know that (l1/l2)^2 = A1/A2
Is there any relationship between the (a)ratio of the lengths and (b)ratio of the Areas with ratio of the Volumes?
http://www.nctm.org/standards/content.aspx?id=25097