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Stretching and Shrinking Procedural Guide
1. In similar figures:
a. ANGLES stay the same
b. Side Lengths change
2. Types of coordinate rules and their effect on similar figures:
a. When ‘x’ and ‘y’ are multiplied by the same number = they stay
similar
b. When ‘x’ and ‘y’ are multiplied by different numbers = they are no
longer similar
3. Coordinate rules and their effect continued
x- coordinate
When ‘x’ is added by a number = moves figure to the right
When ‘x’ is subtracted by a number = moves figure to the left
y-coordinate
When ‘y’ is added by a number = moves figure up
When ‘y’ is subtracted by a number = moves figure down
4. Writing a rule given x and y coordinates
a. Choose corresponding points, write the coordinates down
Ex: Original
Image
(2, 4)
(3, 6)
b. Divide your corresponding coordinates – 3 ÷2 and 6÷4 = 1.5
c. The answer of 1.5 is the rule/scale factor:
Original
Image
(x, y)
(1.5x, 1.5y)
5. Scale Factor (Definition and Example)
Scale Factor the ratio used to enlarge or reduce similar figures. The
difference in the measurement of 2 figures that is similar.
*In order to find scale factor: Divide corresponding side lengths of two similar
figures
If you are making: a figure larger, the SF is greater than > 1
If you are making a figure smaller, the SF is less than < 1
6. How can you find the scale factor & side lengths from a smaller figure to a
larger figure (Give an example)
New
Original
x
1
12
4
New
Original
x
1
12
=
Scale factor = 3
4
Side length = 3
(3 x 1)
Cross multiply:
4x = 12
Divide by 4:
4÷4 12÷4
X=3
7. How can you find the scale factor and side lengths from a larger figure to
a smaller figure? (Give an example)
Original
New
Scale Factor: 2
1
2
x
5
Original
New
2 = 1
5
x
2x = 5
x=2.5
Side Length = 2.5
7. Give a formula and example for:
a. Perimeter and scale factor- add all sides/ multiply it with
Scale Factor
b. Area and scale factorRectangle= A = l x w
Triangle = A = ½ bh
8. Ratio within similar figures (definition and example)
Ratio= A comparison of two quantities (often written as a fraction)
Can use a ratio to see if figures are similar:
Within Ratio
Ratios within the same figure
2
4
4
2 or 1 (1:2)
4 2
4 = 2 (1:2)
8 4
They are similar!
8
1 or (1:4)
4
Between Ratio:
Ratios between figures
3 = 1 (1:4)
12 4
4
1
3
12
They are similar!
1 and 4 are corresponding sides
3 and 12 are corresponding sides
9. Difference between Ratio and scale factor
Scale Factor- how much one figure increases or decreases
Ratio- Compares lengths between and within figures
10.
Adjacent and Congruent (definitions)
Adjacent = next to each other
congruent = means equal (sides, angles)
*When 2 figures are congruent their sides are equal
Complementary and Supplementary Angles:
Complementary= two angles whose sum measures 90˚
Supplementary = two angles whose sum measures 180˚
11.
Find the height using the following: (draw diagram, write formula
and example
Shadow and similar figure:
*USE CROSS MULTIPLICATION
New is always the image that has x
Original has all it’s measurements
Original
New
Mirror and similar figure
These are 2 similar triangles!
Modified by McDonald