Answer:
1. Yes
2. Yes
3. No
Step-by-step explanation:
Given
Rectangle A:
![Length = 12; Width = 8](https://tex.z-dn.net/?f=Length%20%3D%2012%3B%20Width%20%3D%208)
Rectangle B:
![Length = 15; Width = 10](https://tex.z-dn.net/?f=Length%20%3D%2015%3B%20Width%20%3D%2010)
Rectangle C:
![Length = 30; Width = 15](https://tex.z-dn.net/?f=Length%20%3D%2030%3B%20Width%20%3D%2015)
Solving (1): Is Rectangle A a scaled copy of Rectangle B?
To do this, we simply determine the ratio of the length and width of both rectangles;
i.e.
![Ratio = \frac{A}{B}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7BA%7D%7BB%7D)
For Length:
![Ratio = \frac{12}{15}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7B12%7D%7B15%7D)
![Ratio = 0.8](https://tex.z-dn.net/?f=Ratio%20%3D%200.8)
For Width:
![Ratio = \frac{8}{10}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7B8%7D%7B10%7D)
![Ratio = 0.8](https://tex.z-dn.net/?f=Ratio%20%3D%200.8)
Since both ratios are the same, then this statement is true
Solving (2): Is Rectangle B a scaled copy of Rectangle A?
This is the inverse of (1) calculated above.
Since (1) is true, then (2) is also true
3. Is Rectangle A a scaled copy of Rectangle C?
To do this, we simply determine the ratio of the length and width of both rectangles;
i.e.
![Ratio = \frac{A}{C}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7BA%7D%7BC%7D)
For Length:
![Ratio = \frac{12}{30}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7B12%7D%7B30%7D)
![Ratio = 0.4](https://tex.z-dn.net/?f=Ratio%20%3D%200.4)
For Width:
![Ratio = \frac{8}{15}](https://tex.z-dn.net/?f=Ratio%20%3D%20%5Cfrac%7B8%7D%7B15%7D)
![Ratio = 0.53](https://tex.z-dn.net/?f=Ratio%20%3D%200.53)
Since both ratios are the not same, then this statement is false