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.
[tex]k = \frac{DF}{BA} = \frac{FE}{AC} = \frac{DE}{BC}[/tex]
[tex]k = \frac{6}{3} = \frac{8}{4} = \frac{10}{5}[/tex]
[tex]k = 2=2=2[/tex]
[tex]k = 2[/tex]
The scale factor is 2
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.
[tex]k = \frac{KN}{GJ}[/tex]
[tex]k = \frac{6}{4}[/tex]
[tex]k = 1.5[/tex]
The scale factor is 1.5
