Name_________________________________________________________Date____________________________Color__________________
Scaling up and Down
With Dan Meyers’s “Shrinking Dollar”, we worked with images (or copies) that were similar to the
original dollar bill. Those copies were smaller than the original. Now we will work with some images (or
drawings) that are smaller than an original and some images that are larger than the original.
When we study similar figures, we often compare their sides and angles. To compare the parts correctly,
mathematicians use the terms Corresponding Sides and Corresponding Angles.
In every pair of similar figures, each side of one figure has a corresponding side in the other figure. To
determine the corresponding sides, look for the sides whose positions are similar to each other, even
though one is in the small triangle and the other is in the large triangle.
Also, each angle has a corresponding angle. To determine the corresponding angles, look for the angles
whose sizes are similar to each other, even though one is in the small triangle and the other is in the large
triangle.
1) These triangles have 3 sets of corresponding angles.
a) Angle A in the small triangle corresponds with
Angle _____ in the large triangle.
b) Angle B in the small triangle corresponds with Angle
_____ in the large triangle.
c) Angle C in the small triangle corresponds with Angle
_____ in the large triangle.
2) These triangles also have 3 sets of corresponding sides.
a) Side AB in the small triangle corresponds with
Side _____ in the large triangle.
b) Side BC in the small triangle corresponds with
Side _____ in the large triangle.
c) Side CA in the small triangle corresponds with
Side _____ in the large triangle.
Daphne belongs to the Mystery Club. She designs “Super Sleuth” as the club’s logo.
Then she decides to make a copy of “Super Sleuth” with the size factor set at 75%.
After that, she makes a copy with a setting of 150%.
The results are shown below:
3) Compare the three drawings.
a) How do the side lengths in the smaller copy
compare to the
corresponding side lengths in the original figure?
Be specific!
b) How do the angles in the smaller copy
compare to the corresponding angle measures in
the original figure? Be specific!
compare
c) How do the side lengths in the larger copy
compare to the corresponding side lengths in
the original figure? Be specific!
d) How do the angles in the larger copy compare
to the corresponding angle measures in the
original figure? Be specific!
4) a) How does the perimeter of the triangle in
each copy compare to the perimeter of the
triangle in the original? Be specific!
b) How does the area of the triangle in each
copy compare to the area of the triangle in the
original? Be specific!
5) While shopping for sneakers, Ling finds two pairs she likes. One pair costs $55 and the other costs
$165. She makes the following statements about the prices.
“The expensive sneakers cost $110 more than the cheaper sneakers.”
“The cost of the expensive sneakers in 300% of the cost of the cheaper sneakers.”
“The cheaper sneakers are
the cost of the expensive sneakers.”
a) Are all her statements accurate? Explain.
b) How are the comparison methods Ling uses like the methods you use to compare the sizes and
shapes of similar figures?
c) Which statements are appropriate for comparing the size and shape of an image to the original
figure? Explain.