Answer:
(a) Similar polygons; scale factor is 2
(b) Similar polygons; scale factor is 1.5
Step-by-step explanation:
Given
See attachment for polygons
Required
Determine if they are similar or not
Solving (a): The triangle
The angles in both triangles show that the triangles are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
![k = \frac{DF}{BA} = \frac{FE}{AC} = \frac{DE}{BC}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7BDF%7D%7BBA%7D%20%3D%20%5Cfrac%7BFE%7D%7BAC%7D%20%3D%20%5Cfrac%7BDE%7D%7BBC%7D)
![k = \frac{6}{3} = \frac{8}{4} = \frac{10}{5}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B6%7D%7B3%7D%20%3D%20%5Cfrac%7B8%7D%7B4%7D%20%3D%20%5Cfrac%7B10%7D%7B5%7D)
![k = 2=2=2](https://tex.z-dn.net/?f=k%20%3D%202%3D2%3D2)
![k = 2](https://tex.z-dn.net/?f=k%20%3D%202)
<em>The scale factor is 2</em>
<em />
Solving (b): The trapezium
The angles in both trapeziums show that the trapeziums are similar
To calculate the scale factor (k), we simply take corresponding sides.
i.e.
![k = \frac{KN}{GJ}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7BKN%7D%7BGJ%7D)
![k = \frac{6}{4}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B6%7D%7B4%7D)
![k = 1.5](https://tex.z-dn.net/?f=k%20%3D%201.5)
<em>The scale factor is 1.5</em>