Answer:
(c) [tex]\triangle ABC[/tex] to [tex]\triangle EDC[/tex] by AA
Step-by-step explanation:
Given
See attachment for triangles
Required
The relationship between both triangles
First, we determine the corresponding sides.
The corresponding sides will be determined based on the length of each side (i.e. bigger sides correspond while smaller sides correspond).
So, we have:
[tex]AC\ to\ EC[/tex]
[tex]BC\ to\ DC[/tex]
Next, is to name the triangle base on the corresponding sides
The names will be: [tex]\triangle ABC[/tex] and [tex]\triangle EDC[/tex]
Lastly, is to check the scale ratio (k).
For both triangles to correspond, the scale ratio must be the same
So:
[tex]k = \frac{EC}{AC} = \frac{DC}{BC}[/tex]
[tex]k = \frac{8}{6} = \frac{12}{9}[/tex]
[tex]k = \frac{4}{3} = \frac{4}{3}[/tex]
[tex]k = \frac{4}{3}[/tex]
Hence, the theorem is: [tex]\triangle ABC[/tex] to [tex]\triangle EDC[/tex] by AA
